Stability of bimodal planar linear switched systems

Abstract

We study dynamics of a bimodal planar linear switched system with both subsystems Hurwitz stable. We give dwell time bounds so that the switched system is asymptotically stable. These bounds obtained are in terms of certain smooth functions of the eigenvalues and (generalized) eigenvectors of the subsystem matrices. The results are extended to a special class of symmetric bilinear systems. The results are also extended to a multimodal planar linear switched system in which the switching is governed by an undirected star graph. For such systems, dwell time bounds are obtained as solutions of a minimax optimization problem.