Existence of a common quadratic lyapunov function for discrete switched linear systems with m stable subsystems

摘要

The problem on the existence of a common quadratic Lyapunov function (CQLF) for discrete switched linear systems with m stable subsystems is considered. System matrices are Schur stable. A necessary condition for the existence of a CQLF and a sufficient condition for the non-existence of a CQLF are derived, respectively. Numerical examples are presented to illustrate the results.