On Second-Moment Stability of Discrete-Time Linear Systems with General Stochastic Dynamics

TL;DR

This paper introduces a unified framework for analyzing second-moment stability in discrete-time linear systems with various stochastic dynamics, deriving Lyapunov inequalities and applying them to different stochastic processes.

Contribution

It presents a novel, comprehensive approach that encompasses general stochastic processes for stability analysis, extending existing methods with new Lyapunov-based conditions.

Findings

Unified stability conditions for general stochastic dynamics

Derivation of Lyapunov inequalities applicable to various processes

Application examples demonstrating framework effectiveness

Abstract

This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics, and associated Lyapunov inequalities are derived. Any type of stochastic process can be dealt with as a special case in our framework for determining system dynamics, and our results together with assumptions (i.e., restrictions) on the process immediately lead us to stability conditions for the corresponding special stochastic systems. As a demonstration of usefulness of such a framework, three selected applications are also provided.