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Linear Models for the Prediction of the Genetic Merit of Animals
by Raphael A Mrode Ivan PocrnicFundamental to any livestock improvement programme by animal scientists, is the prediction of genetic merit in the offspring generation for desirable production traits such as increased growth rate, or superior meat, milk and wool production. Covering the foundational principles on the application of linear models for the prediction of genetic merit in livestock, this new edition is fully updated to incorporate recent advances in genomic prediction approaches, genomic models for multi-breed and crossbred performance, dominance and epistasis. It provides models for the analysis of main production traits as well as functional traits and includes numerous worked examples. For the first time, R codes for key examples in the textbook are provided online. The book covers: - The relationship between the genome and the phenotype. - BLUP models for various livestock data and structure. - Incorporation of related ancestral parents and metafounders in prediction models. - Models for survival analysis and social interaction. - Advancements in genomic prediction approaches and selection. - Genomic models for multi-breed and crossbred performance. - Models for non-additive genetic effects including dominance and epistasis. - Estimation of genetic parameters including Gibbs sampling approaches. - Computation methods for solving linear mixed model equations. Suitable for graduate and postgraduate students, researchers and lecturers of animal breeding, genetics and genomics, this established textbook provides a thorough grounding in both the basics and in new developments of linear models and animal genetics.
Linear Multivariable Control Engineering Using GNU Octave
by Wolfgang BorutzkyThis textbook presents an in-depth introductory survey of several fundamental advanced control concepts and techniques all ranging from modern ideas. The book emphasizes ideas, an understanding of key concepts, methodologies, and results. In line with this, the book addresses master’s students in the overlap of engineering and computer science as well as engineers working in various application fields and interested in useful control techniques and less in system theories appealing from a mathematical point of view. The book aims to show what methods and results learned for single-variable systems are also applicable to multivariable systems, what is different and why. The structured text covers a broad spectrum of topics from decentralized control to the use of linear matrix inequalities (LMIs). Methods and results are illustrated by many examples and using free, open source mathematical software, predominately GNU Octave. In some cases, the free mathematical software package Scilab is also used. The book features exercises and examples throughout.
Linear Optimization and Duality: A Modern Exposition
by Craig A. ToveyLinear Optimization and Dualiyy: A Modern Exposition departs from convention in significant ways. Standard linear programming textbooks present the material in the order in which it was discovered. Duality is treated as a difficult add-on after coverage of formulation, the simplex method, and polyhedral theory. Students end up without knowing duality in their bones. This text brings in duality in Chapter 1 and carries duality all the way through the exposition. Chapter 1 gives a general definition of duality that shows the dual aspects of a matrix as a column of rows and a row of columns. The proof of weak duality in Chapter 2 is shown via the Lagrangian, which relies on matrix duality. The first three LP formulation examples in Chapter 3 are classic primal-dual pairs including the diet problem and 2-person zero sum games. For many engineering students, optimization is their first immersion in rigorous mathematics. Conventional texts assume a level of mathematical sophistication they don’t have. This text embeds dozens of reading tips and hundreds of answered questions to guide such students. Features Emphasis on duality throughout Practical tips for modeling and computation Coverage of computational complexity and data structures Exercises and problems based on the learning theory concept of the zone of proximal development Guidance for the mathematically unsophisticated reader About the Author Craig A. Tovey is a professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. Dr. Tovey received an AB from Harvard College, an MS in computer science and a PhD in operations research from Stanford University. His principal activities are in operations research and its interdisciplinary applications. He received a Presidential Young Investigator Award and the Jacob Wolfowitz Prize for research in heuristics. He was named an Institute Fellow at Georgia Tech, and was recognized by the ACM Special Interest Group on Electronic Commerce with the Test of Time Award. Dr. Tovey received the 2016 Golden Goose Award for his research on bee foraging behavior leading to the development of the Honey Bee Algorithm.
Linear Parameter-Varying Control for Engineering Applications
by Andrew P. White Guoming Zhu Jongeun ChoiThe subject of this brief is the application of linear parameter-varying (LPV) control to a class of dynamic systems to provide a systematic synthesis of gain-scheduling controllers with guaranteed stability and performance. An important step in LPV control design, which is not well covered in the present literature, is the selection of weighting functions. The proper selection of weighting functions tunes the controller to obtain the desired closed-loop response. The selection of appropriate weighting functions is difficult and sometimes appears arbitrary. In this brief, gain-scheduling control with engineering applications is covered in detail, including the LPV modeling, the control problem formulation, and the weighting function optimization. In addition, an iterative algorithm for obtaining optimal output weighting functions with respect to the H2 norm bound is presented in this brief. Using this algorithm, the selection of appropriate weighting functions becomes an automatic process. The LPV design and control synthesis procedures in this brief are illustrated using: * air-to-fuel ratio control for port-fuel-injection engines; * variable valve timing control; and * application to a vibration control problem. After reading this brief, the reader will be able to apply its concepts to design gain-scheduling controllers for their own engineering applications. This brief provides detailed step-by-step LPV modeling and control design strategies along with an automatic weight-selection algorithm so that engineers can apply state-of-the-art LPV control synthesis to solve their own engineering problems. In addition, this brief should serve as a bridge between the H-infinity and H2 control theory and the real-world application of gain-scheduling control.
Linear Parameter-Varying Control: Theory and Application to Automotive Systems
by Olivier SenameAn authoritative new exploration of the latest theoretical and applied advances in Linear Parameter-Varying systems In Linear Parameter-Varying Control: Theory and Application to Automotive Systems, distinguished researcher Dr. Olivier Sename delivers a comprehensive and up-to-date discussion of the theoretical aspects and real applications of Linear Parameter-Varying (LPV) control, with a strong focus on systems theory and in real automotive systems. The author covers the primary methods used to model, control, and analyze LPV systems, and illustrates how to model those systems using examples. This book covers developing adaptive LPV control using the provided recipes as guides and contextual aids as well as discovering effective methods to design LPV controllers that have already been validated through real applications. Readers will also find: A thorough introduction to vehicle dynamics control in automated vehicles, as well as suspension controlComprehensive explorations of LPV systems modelling, including dynamical systemsPractical discussions of the properties of LPV systems, including controllability, observability, and stabilityComplete treatments of LPV systems control, including state feedback control and dynamic output feedback LPV control Perfect for researchers and students with an interest in vehicle dynamics, Linear Parameter-Varying Control will also benefit postgraduate and PhD students, control engineers, and academics teaching control theory and applications courses.
Linear Parameter-Varying and Time-Delay Systems
by Corentin BriatThis book provides an introduction to the analysis and control of Linear Parameter-Varying Systems and Time-Delay Systems and their interactions. The purpose is to give the readers some fundamental theoretical background on these topics and to give more insights on the possible applications of these theories. This self-contained monograph is written in an accessible way for readers ranging from undergraduate/PhD students to engineers and researchers willing to know more about the fields of time-delay systems, parameter-varying systems, robust analysis, robust control, gain-scheduling techniques in the LPV fashion and LMI based approaches. The only prerequisites are basic knowledge in linear algebra, ordinary differential equations and (linear) dynamical systems. Most of the results are proved unless the proof is too complex or not necessary for a good understanding of the results. In the latter cases, suitable references are systematically provided. The first part pertains on the representation, analysis and control of LPV systems along with a reminder on robust analysis and control techniques. The second part is concerned with the representation and analysis of time-delay systems using various time-domain techniques. The third and last part is devoted to the representation, analysis, observation, filtering and control of LPV time-delay systems. The book also presents many important basic and advanced results on the manipulation of LMIs.
Linear Polyurethanes: Synthesis Methods, Chemical Structures, Properties and Applications
by Piotr KrolThis volume describes in detail the mechanisms of the diisocyanates and polyols polyaddition process as well as its kinetic and process aspects important for obtaining linear polyurethanes. General kinetics of the process and its experimental verification, using GPC chromatography as well as NMR spectroscopy and MALDI-ToF spectrometry, are presente
Linear Programming and Algorithms for Communication Networks: A Practical Guide to Network Design, Control, and Management
by Eiji OkiExplaining how to apply to mathematical programming to network design and control, Linear Programming and Algorithms for Communication Networks: A Practical Guide to Network Design, Control, and Management fills the gap between mathematical programming theory and its implementation in communication networks. From the basics all the way through to m
Linear Programming and Generalizations
by Eric V. DenardoThis book on constrained optimization is novel in that it fuses these themes: * use examples to introduce general ideas; * engage the student in spreadsheet computation; * survey the uses of constrained optimization;. * investigate game theory and nonlinear optimization, * link the subject to economic reasoning, and * present the requisite mathematics. Blending these themes makes constrained optimization more accessible and more valuable. It stimulates the student's interest, quickens the learning process, reveals connections to several academic and professional fields, and deepens the student's grasp of the relevant mathematics. The book is designed for use in courses that focus on the applications of constrained optimization, in courses that emphasize the theory, and in courses that link the subject to economics.
Linear Stochastic Systems
by Anders Lindquist Giorgio PicciThis book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others. Problems concerning the filtering and modeling of stationary random signals and systems have also been addressed and studied, fostered by the advent of modern digital computers, since the fundamental work of R. E. Kalman in the early 1960s. The book offers a unified and logically consistent view of the subject based on simple ideas from Hilbert space geometry and coordinate-free thinking. In this framework, the concepts of stochastic state space and state space modeling, based on the notion of the conditional independence of past and future flows of the relevant signals, are revealed to be fundamentally unifying ideas. The book, based on over 30 years of original research, represents a valuable contribution that will inform the fields of stochastic modeling, estimation, system identification, and time series analysis for decades to come. It also provides the mathematical tools needed to grasp and analyze the structures of algorithms in stochastic systems theory.
Linear Synchronous Motors: Transportation and Automation Systems, Second Edition (Electric Power Engineering Series)
by Jacek F. Gieras Zbigniew J. Piech Bronislaw TomczukConsidered to be the first book devoted to the subject, Linear Synchronous Motors: Transportation and Automation Systems, Second Edition evaluates the state of the art, demonstrating the technological innovations that are improving the design, construction, and performance of modern control systems. This new edition not only illustrates the development of linear synchronous motor drives, but it also discusses useful techniques for selecting a motor that will meet the specific requirements of linear electrical drives. New Features for the Second Edition: Several updated and expanded sections, as well as two new chapters on FEM Even more numerical examples, calculations, and mathematical models Broadened target audience that includes researchers, scientists, students, and more Evaluating trends and practical techniques for achieving optimal system performance, the authors showcase ready-to-implement solutions for common roadblocks in this process. The book presents fundamental equations and calculations used to determine and evaluate system operation, efficiency, and reliability, with an exploration of modern computer-aided design of linear synchronous motors, including the finite element approach. It covers topics such as linear sensors and stepping motors, magnetic levitation systems, elevators, and factory automation systems. It also features case studies on flat PM, tubular PM, air-cored, and hybrid linear synchronous motors, as well as 3D finite element method analysis of tubular linear reluctance motors, and linear oscillatory actuators. With such an exceptional presentation of practical tools and conceptual illustrations, this volume is an especially powerful resource. It will benefit readers from all walks by providing numerical examples, models, guidelines, and diagrams to help develop a clear understanding of linear synchronous motor operations, characteristics, and much more.
Linear Systems
by S. P. Bhattacharyya L. H. Keel D. N. MohsenizadehThis brief presents recent results obtained on the analysis, synthesis and design of systems described by linear equations. It is well known that linear equations arise in most branches of science and engineering as well as social, biological and economic systems. The novelty of this approach is that no models of the system are assumed to be available, nor are they required. Instead, a few measurements made on the system can be processed strategically to directly extract design values that meet specifications without constructing a model of the system, implicitly or explicitly. These new concepts are illustrated by applying them to linear DC and AC circuits, mechanical, civil and hydraulic systems, signal flow block diagrams and control systems. These applications are preliminary and suggest many open problems. The results presented in this brief are the latest effort in this direction and the authors hope these will lead to attractive alternatives to model-based design of engineering and other systems.
Linear Systems
by Godfrey K. Kwan Henri BourlèsLinear systems have all the necessary elements (modeling, identification, analysis and control), from an educational point of view, to help us understand the discipline of automation and apply it efficiently. This book is progressive and organized in such a way that different levels of readership are possible. It is addressed both to beginners and those with a good understanding of automation wishing to enhance their knowledge on the subject. The theory is rigorously developed and illustrated by numerous examples which can be reproduced with the help of appropriate computation software. 60 exercises and their solutions are included to enable the readers to test and enhance their knowledge.
Linear Systems Theory
by João P. HespanhaLinear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. In this textbook, João Hespanha covers the key topics of the field in a unique lecture-style format, making the book easy to use for instructors and students. He looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization, and examines advanced foundational topics such as multivariable poles and zeros, and LQG/LQR.The textbook presents only the most essential mathematical derivations, and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these important tools. The balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review. Solutions to the theoretical and computational exercises are also available for instructors.Easy-to-use textbook in unique lecture-style format Sidebars explain topics in further detail Annotated proofs and discussions of MATLAB commands Balanced chapters can each be taught in two hours of course lecture Solutions to exercises available to instructors
Linear Systems Theory (Systems Engineering Ser.)
by Ferenc SzidarovszkyThis second edition comprehensively presents important tools of linear systems theory, including differential and difference equations, Laplace and Z transforms, and more.Linear Systems Theory discusses:Nonlinear and linear systems in the state space form and through the transfer function methodStability, including marginal stability, asymptotical stability, global asymptotical stability, uniform stability, uniform exponential stability, and BIBO stabilityControllabilityObservabilityCanonical formsSystem realizations and minimal realizations, including state space approach and transfer function realizationsSystem designKalman filtersNonnegative systemsAdaptive controlNeural networksThe book focuses mainly on applications in electrical engineering, but it provides examples for most branches of engineering, economics, and social sciences.What's New in the Second Edition?Case studies drawn mainly from electrical and mechanical engineering applications, replacing many of the longer case studiesExpanded explanations of both linear and nonlinear systems as well as new problem sets at the end of each chapterIllustrative examples in all the chaptersAn introduction and analysis of new stability conceptsAn expanded chapter on neural networks, analyzing advances that have occurred in that field since the first editionAlthough more mainstream than its predecessor, this revision maintains the rigorous mathematical approach of the first edition, providing fast, efficient development of the material.Linear Systems Theory enables its reader to develop his or her capabilities for modeling dynamic phenomena, examining their properties, and applying them to real-life situations.
Linear Systems: Non-Fragile Control and Filtering (Automation And Control Engineering Ser. #40)
by Xiang-Gui Guo Guang-Hong Yang Wei-Wei Che Wei GuanLinear Systems: Non-Fragile Control and Filtering presents the latest research results and a systematic approach to designing non-fragile controllers and filters for linear systems. The authors combine the algebraic Riccati technique, the linear matrix inequality (LMI) technique, and the sensitivity analysis method to establish a set of new non-fragile (insensitive) control methods. This proposed method can optimize the closed-loop system performance and make the designed controllers or filters tolerant of coefficient variations in controller or filter gain matrices. A Systematic Approach to Designing Non-Fragile Controllers and Filters for Linear Systems The text begins with developments and main research methods in non-fragile control. It then systematically presents novel methods for non-fragile control and filtering of linear systems with respect to additive/multiplicative controller/filter gain uncertainties. The book introduces the algebraic Riccati equation technique to solve additive/multiplicative norm-bounded controller/filter gain uncertainty, and proposes a structured vertex separator to deal with the numerical problem resulting from interval-bounded coefficient variations. It also explains how to design insensitive controllers and filters in the framework of coefficient sensitivity theory. Throughout, the book includes numerical examples to demonstrate the effectiveness of the proposed design methods. More Effective Design Methods for Non-Fragile Controllers and Filters The design and analysis tools described will help readers to better understand and analyze parameter uncertainties and to design more effective non-fragile controllers and filters. Providing a coherent approach, this book is a valuable reference for researchers, graduate students, and anyone who wants to explore the area of non-fragile control and filtering.
Linear Systems: Optimal and Robust Control
by Alok SinhaBalancing rigorous theory with practical applications, Linear Systems: Optimal and Robust Control explains the concepts behind linear systems, optimal control, and robust control and illustrates these concepts with concrete examples and problems.Developed as a two-course book, this self-contained text first discusses linear systems, incl
Linear Transformation: Examples and Solutions (Mathematical Engineering, Manufacturing, and Management Sciences)
by Nita H. Shah Urmila B. ChaudhariThis book introduces linear transformation and its key results, which have applications in engineering, physics, and various branches of mathematics. Linear transformation is a difficult subject for students. This concise text provides an in-depth overview of linear trans-formation. It provides multiple-choice questions, covers enough examples for the reader to gain a clear understanding, and includes exact methods with specific shortcuts to reach solutions for particular problems. Research scholars and students working in the fields of engineering, physics, and different branches of mathematics need to learn the concepts of linear transformation to solve their problems. This book will serve their need instead of having to use the more complex texts that contain more concepts then needed. The chapters mainly discuss the definition of linear transformation, properties of linear transformation, linear operators, composition of two or more linear transformations, kernels and range of linear transformation, inverse transformation, one-to-one and onto transformation, isomorphism, matrix linear transformation, and similarity of two matrices.
Linear and Integer Optimization: Theory and Practice, Third Edition (Advances in Applied Mathematics)
by Gerard Sierksma Yori ZwolsPresenting a strong and clear relationship between theory and practice, Linear and Integer Optimization: Theory and Practice is divided into two main parts. The first covers the theory of linear and integer optimization, including both basic and advanced topics. Dantzig's simplex algorithm, duality, sensitivity analysis, integer optimization models
Linear and Non-Linear Deformations of Elastic Solids
by Arabinda Roy Rasajit Kumar BeraLinear and Non-Linear Deformations of Elastic Solids aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics. Broadly classified into two parts, it includes crack, contact, scattering and wave propagation in linear elastic solids and bending vibration, stability in non-linear elastic solids supported by MATLAB examples. This book is aimed at graduate students and researchers in applied mathematics, solid mechanics, applied mechanics, structural mechanics and includes comprehensive discussion of related analytical/numerical methods.
Linear and Non-Linear System Theory
by T Thyagarajan D KalpanaLinear and Non-Linear System Theory focuses on the basics of linear and non-linear systems, optimal control and optimal estimation with an objective to understand the basics of state space approach linear and non-linear systems and its analysis thereof. Divided into eight chapters, materials cover an introduction to the advanced topics in the field of linear and non-linear systems, optimal control and estimation supported by mathematical tools, detailed case studies and numerical and exercise problems. This book is aimed at senior undergraduate and graduate students in electrical, instrumentation, electronics, chemical, control engineering and other allied branches of engineering. Features Covers both linear and non-linear system theory Explores state feedback control and state estimator concepts Discusses non-linear systems and phase plane analysis Includes non-linear system stability and bifurcation behaviour Elaborates optimal control and estimation
Linear and Non-Linear Video and TV Applications
by Daniel MinoliProvides options for implementing IPv6 and IPv6 multicast in service provider networksNew technologies, viewing paradigms, and content distribution approaches are taking the TV/video services industry by storm. Linear and Nonlinear Video and TV Applications: Using IPv6 and IPv6 Multicast identifies five emerging trends in next-generation delivery of entertainment-quality video. These trends are observable and can be capitalized upon by progressive service providers, telcos, cable operators, and ISPs.This comprehensive guide explores these evolving directions in the TV/video services industry, including worldwide deployment of IPv6, IPTV services, web-produced video content, and the plethora of different screens available, from TV to iPad. It offers practical suggestions as to how these technologies can be implemented in service provider networks to support cost-effective delivery of entertainment, and how new revenue-generating services can be brought to market.Important topics include:Evolving video consumption habits and possible network implicationsAn overview of IPv6 address capabilities, protocols, quality of service (QoS), and moreProcess descriptions of IP multicast and IPv6 multicast approaches and challengesA detailed overview of IPTV systems and technologies, including architectural requirements, QoE and QoS, security and content protection, networks, and moreInternet-based TV technologies: streaming, content distribution networks, P2P networks, and cloud computingNon-traditional video content sources and their implicationsLinear and Nonlinear Video and TV Applications: Using IPv6 and IPv6 Multicast is indispensable reading for planners, CTOs, and engineers at broadcast TV operations, Cable TV operations, satellite operations, Internet and IS providers, telcos, and wireless providers.
Linear and Non-linear Numerical Analysis of Foundations
by John W. BullCorrectly understanding, designing and analyzing the foundations that support structures is fundamental to their safety. This book by a range of academic, design and contracting world experts provides a review of the state-of-the-art techniques for modelling foundations using both linear and non linear numerical analysis. It applies to a range of i
Linear and Nonlinear Circuits: Volume 2 (Lecture Notes in Electrical Engineering #620)
by Mauro Parodi Marco StoraceThis book provides readers with the necessary background information and advanced concepts in the field of circuits, at the crossroads between physics, mathematics and system theory. It covers various engineering subfields, such as electrical devices and circuits, and their electronic counterparts. Based on the idea that a modern university course should provide students with conceptual tools to understand the behavior of both linear and nonlinear circuits, to approach current problems posed by new, cutting-edge devices and to address future developments and challenges, the book places equal emphasis on linear and nonlinear, two‐terminal and multi‐terminal, as well as active and passive circuit components. This second volume focuses on dynamical circuits, which are characterized by time evolution and by the concept of state. The content is divided into a set of introductory and a set of advanced‐level topics, mirroring the approach used in the previously published volume. Whenever possible, circuits are compared to physical systems of different natures (e.g. mechanical or biological) that exhibit the same dynamical behavior. The book also features a wealth of examples and numerous solved problems. Further topics, such as a more general framing of linear and nonlinear components, will be discussed in volume 3.
Linear and Nonlinear Control of Small-Scale Unmanned Helicopters
by Ioannis A. Raptis Kimon P. ValavanisThere has been significant interest for designing flight controllers for small-scale unmanned helicopters. Such helicopters preserve all the physical attributes of their full-scale counterparts, being at the same time more agile and dexterous. This book presents a comprehensive and well justified analysis for designing flight controllers for small-scale unmanned helicopters guarantying flight stability and tracking accuracy. The design of the flight controller is a critical and integral part for developing an autonomous helicopter platform. Helicopters are underactuated, highly nonlinear systems with significant dynamic coupling that needs to be considered and accounted for during controller design and implementation. Most reliable mathematical tools for analysis of control systems relate to modern control theory. Modern control techniques are model-based since the controller architecture depends on the dynamic representation of the system to be controlled. Therefore, the flight controller design problem is tightly connected with the helicopter modeling. This book provides a step-by-step methodology for designing, evaluating and implementing efficient flight controllers for small-scale helicopters. Design issues that are analytically covered include: * An illustrative presentation of both linear and nonlinear models of ordinary differential equations representing the helicopter dynamics. A detailed presentation of the helicopter equations of motion is given for the derivation of both model types. In addition, an insightful presentation of the main rotor's mechanism, aerodynamics and dynamics is also provided. Both model types are of low complexity, physically meaningful and capable of encapsulating the dynamic behavior of a large class of small-scale helicopters. * An illustrative and rigorous derivation of mathematical control algorithms based on both the linear and nonlinear representation of the helicopter dynamics. Flight controller designs guarantee that the tracking objectives of the helicopter's inertial position (or velocity) and heading are achieved. Each controller is carefully constructed by considering the small-scale helicopter's physical flight capabilities. Concepts of advanced stability analysis are used to improve the efficiency and reduce the complexity of the flight control system. Controller designs are derived in both continuous time and discrete time covering discretization issues, which emerge from the implementation of the control algorithm using microprocessors. * Presentation of the most powerful, practical and efficient methods for extracting the helicopter model parameters based on input/output responses, collected by the measurement instruments. This topic is of particular importance for real-life implementation of the control algorithms. This book is suitable for students and researches interested in the development and the mathematical derivation of flight controllers for small-scale helicopters. Background knowledge in modern control is required.