Stability of a Switched System

Stability Condition via Eigenvalues and Dwell Times

Abstract

We consider stability of a switched system which consists of multiple linear time-invariant subsystems. It is assumed that the state coefficient matrices of the subsystems belong to a certain class and the subsystems are switched according to their dwell times. We present a necessary and sufficient condition for stability of the switched system in terms of eigenvalues of the coefficient matrices and the dwell times of the subsystems.