Abstract
The objective of this paper is to extend the frequency domain critorion for predicting the stability of a clas9 of linear time-varying-gain systems, subject to white Gaussian noise input disturbance. It is shown that, if the noise is linearly related to the state of the system, a relatively simple frequency-domain inequality, that guarantees asymptotic stability with probability one (ASWPI) of the system, exists. The stochastic version of the second method of Lyapunov, along with a modified Moyer-Kalman-Yakubovich (M.K.Y.) lemma is used to derive such a condition. Finally geometric interpretation of the criterion is presented.
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