Abstract
This paper presents consideration on the mean square stability of a linear continuous time system perturbed by a Gaussian white noise linearly dependent on the state variables. A necessary and sufficient condition is given for the system's stability, and some sufficient conditions which are easier to use are also given. Similar stability conditions are presented for the linear discrete time systems with a state dependent noise.
The results obtained here are generalizations of earlier results given by Willems, Kleinman, McLane, etc.
