Time-Dependent Switched Discrete-Time Linear Systems: Control and Filtering

By: Lixian Zhang and Yanzheng Zhu and Peng Shi and Qiugang Lu

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Synopsis: Thisbook focuses on the basic control and filtering synthesis problems fordiscrete-time switched linear systems under time-dependent switching signals. Chapter 1, as an introduction of the book, gives the backgrounds andmotivations of switched systems, the definitions of the typical time-dependentswitching signals, the differences and links to other types of systems withhybrid characteristics and a literature review mainly on the control andfiltering for the underlying systems. By summarizing the multiple Lyapunov-likefunctions (MLFs) approach in which different requirements on comparisons ofLyapunov function values at switching instants, a series of methodologies are developed for the issues onstability and stabilization, and l2-gainperformance or tube-based robustness for l∞disturbance, respectively, in Chapters 2 and 3. Chapters 4 and 5 are devoted tothe control and filtering problems for the time-dependent switched linearsystems with either polytopic uncertainties or measurable time-varyingparameters in different sense of disturbances. The asynchronous switchingproblem, where there is time lag between the switching of the currentlyactivated system mode and the controller/filter to be designed, is investigatedin Chapter 6. The systems with various time delays under typical time-dependentswitching signals are addressed in Chapter 7.