TY - CHAP
T1 - Stability and stabilization
AU - Zhang, Lixian
AU - Zhu, Yanzheng
AU - Shi, Peng
AU - Lu, Qiugang
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.
PY - 2016
Y1 - 2016
N2 - 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 μ -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.
AB - 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 μ -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.
UR - https://www.scopus.com/pages/publications/85028999408
U2 - 10.1007/978-3-319-28850-5_2
DO - 10.1007/978-3-319-28850-5_2
M3 - 章节
AN - SCOPUS:85028999408
T3 - Studies in Systems, Decision and Control
SP - 27
EP - 58
BT - Studies in Systems, Decision and Control
PB - Springer International Publishing
ER -