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

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.