Construction of a Lyapunov Function for a Linear Large-Scale Periodic System With Possibly Unstable Subsystems

Abstract

This article proposes an approach to construct a Lyapunov function for a linear large-scale periodic system. In this case, in contrast to various variants of small-gain stability conditions for large-scale systems, the presence of the asymptotic stability property of independent subsystems is not assumed. To analyze the asymptotic stability of a large-scale system, the direct Lyapunov method is used in combination with the discretization method and identities of the commutator calculus. The main results are illustrated by means of examples. (C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.