Stability criteria for discrete-time systems with colored multiplicative noise

Often a mathematical model of a dynamical system requires the consideration of uncertain elements. Historically, emphasis has been placed on studying systems in which disturbances enter additively, but many control problems include disturbances that can be more naturally modeled as uncertain (time-varying) multiplicative gains. If the multiplicative gain is of the white noise type, necessary and sufficient conditions for the stability of many of these systems have been derived previously. In this article, we develop conditions for the stability of some discrete-time systems containing multiplicative colored noise. Discrete-time systems in which the colored noise is generated nonrecursively are studied. Necessary and sufficient conditions for their mean square stability have been obtained, and numerical solutions are provided for cases in which the colored noise parameter is generated recursively.