On common quadratic Lyapunov functions for dynamic normal switched systems

Abstract

In this paper, we investigate when the Euclidean norm is a quadratic Lyapunov function for linear dynamic equations, and use this result to determine the existence of a stabilizing switching pattern for switched systems comprised of normal subsystem matrices. We then expand these results to establish sufficient conditions for the existence of common quadratic Lyapunov functions other than the Euclidean norm for switched systems comprised of normal matrices.