On Lyapunov functions for random one‐sided systems in terms of nonuniform exponential stability with applications

Abstract

In this study, we investigate the nonuniform exponential stability and nonuniform exponential instability concepts for a linear random one‐sided system. We derive necessary and sufficient conditions for these concepts. As an extension for this study, we establish Lyapunov‐type characterizations using Lyapunov functions and Lyapunov norms. Additionally, we illustrate the essential properties that are derived in these directions for the adjoint and inverse systems associated for the original linear random one‐sided system.