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

This book focuses on the basic control and filtering synthesis problems for discrete-time switched linear systems under time-dependent switching signals. Chapter 1, as an introduction of the book, gives the backgrounds and motivations of switched systems, the definitions of the typical time-dependent switching signals, the differences and links to other types of systems with hybrid characteristics and a literature review mainly on the control and filtering for the underlying systems. By summarizing the multiple Lyapunov-like functions (MLFs) approach in which different requirements on comparisons of Lyapunov function values at switching instants, a series of  methodologies are developed for the issues on stability and stabilization, and l2-gain performance or tube-based robustness for l∞ disturbance, respectively, in Chapters 2 and 3. Chapters 4 and 5 are devoted to the control and filtering problems for the time-dependent switched linear systems with either polytopic uncertainties or measurable time-varying parameters in different sense of disturbances. The asynchronous switching problem, where there is time lag between the switching of the currently activated system mode and the controller/filter to be designed, is investigated in Chapter 6. The systems with various time delays under typical time-dependent switching signals are addressed in Chapter 7.

“This book presents new developments on discrete-time systems with nondeterministic switching parameters. … the book includes recent and original results on control and filtering problems for time-dependent discrete-time switched systems. The solutions of the investigated problems are presented in the form suitable for numerical implementation. The theoretical results are validated by examples from various engineering areas of interest.” (Adrian-Mihail Stoica, Mathematical Reviews, January, 2017)“The present book is confined to discrete-time linear switched control systems having linear state-output functions. … Each chapter is equipped with several references. Moreover, the book contains many figures, tables and examples. The monograph can be recommended for courses in discrete-time linear switched systems.” (Kurt Marti, zbMATH 1356.90003, 2017)