Generalized invariance principles for switched delay systems. (English) Zbl 1216.93090

Liu, Jun; Liu, Xinzhi; Xie, Wei-Chau

IMA J. Math. Control Inf. 28, No. 1, 19-39 (2011).

Summary: The classical LaSalle’s invariance principle for ordinary differential equations is extended to switched delay systems. Generalized invariance principles are established, using both multiple Lyapunov functionals and multiple Lyapunov-Razumikhin functions. As an important application, stability criteria for switched delay systems are obtained.

MSC:

93D30	Lyapunov and storage functions
93C30	Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C15	Control/observation systems governed by ordinary differential equations

Keywords:

switched systems delay systems hybrid systems; invariance principles stability multiple Lyapunov functionals multiple Lyapunov-Razumikhin functions