On stability of linear time-varying stochastic discrete-time systems

Stability conditions are given for time-varying discrete-time linear systems driven by second order noise. We assume that the stochastic system satisfies a prescribed time-average bound on the sum of successive second moments of the state variable. We show that under this and some other mild assumptions, the time-varying system is asymptotically stable. An immediate consequence of the present approach is that the system is also uniformly asymptotically stable provided that the system under investigation is periodic.