Eigenvalue placement for asymptotic stability in piecewise linear switched systems

Abstract

In this paper we provide an eigenvalue placement methodology that guarantees asymptotic stability in a piecewise linear switched system where a lowerbound on the dwell time is known in advance. In particular, considering the case where each subsystem is a linear controllable system, we introduce an algorithm for placing the eigenvalues of each subsystem in such a way that the overall switched system is asymptotically stable. This is obtained defining a relationship between the dwell time and the stability properties of each subsystem. Simulations of a heterogeneous multi-robot system are provided for validation purposes.