Frequency domain stability criteria for stochastic systems

The stability of a class of dynamical systems containing random parameters is investigated. An input-output stability concept is formulated for stochastic systems. The specific class of systems considered consists of those feedback systems whose open loop consists of the cascade of a white noise multiplicative gain and a linear deterministic dynamical system. Necessary and sufficient frequency domain conditions for stability are derived and it is shown that the uncertainty has a destabilizing effect. The resulting stability conditions depend on the open-loop stability, the rms value of the stochastic gain element, and the effective bandwidth of the linear element.