A Bounded Real Lemma for Discrete-time Systems with Stochastic Dynamics

The bounded real lemma for deterministic linear time-invariant systems is known as one of the most important tools in robust stability analysis. A counterpart for systems with stochastic dynamics is considered to be also important, and A.E. Bouhtouri, et al. (1998) have derived it for discrete-time systems with state-dependent noise. However, the class of the systems is restrictive, and has room for generalization. The purpose of this paper is to show the sufficiency for a new bounded real lemma for more general systems with stochastic dynamics determined by an i.i.d. process. The validity of the lemma is demonstrated with numerical examples.