2. Stability and Stabilization

This chapter is devoted to the stability analysis for the four types of time-dependent switched systems. We first summarize the mainly used multiple Lyapunov-like functions (MLFs) approaches, sort out several typical MLFs and review their characteristics. Then, the corresponding methodologies by different MLFs such as switched Lyapunov function, MLFs with \(\mu \)-times increase at switching instants are developed to study the stability conditions for the underlying system with arbitrary switching, dwell time (DT) switching, average dwell time (ADT) switching, persistent dwell time (PDT) switching and their mode-dependent forms, respectively. The generally analytic results in discrete-time context will be concretely formulated in terms of linear matrix equalities (LMIs). Numerical examples are provided to verify the obtained criteria and to compare the four kinds of time-dependent switched systems. The results obtained in this chapter will lay a foundation for future developments in this book.