Switching stabilization and $${ H}_{\varvec{\infty }}$$ H ∞ performance of a class of discrete switched LPV system with unstable subsystems

Abstract

Stability and \(H_\infty \) performance are analyzed in this paper for a class of discrete switched linear parameter-varying (LPV) systems in which all subsystems’ state-space matrices are parametrically affine, and any subsystem is not stable for parameters varying in a convex set. A switching law is designed to stabilize and satisfy the \(H_\infty \) performance of the switched LPV system. By means of the multiple Lyapunov functions method, linear matrix inequality (LMI) conditions for the existence of parameter-dependent Lyapunov functions are proposed. An example shows the effectiveness of the proposed methods.