Abstract
The stability of linear time invariant systems with state dependent noise is considered by McLane and Kleinman, and a stabilizability condition is given by Wonham.
In this paper, exponential asymptotic stability with probability 1 and mean square stability of a linear time-varying system with Gaussian noise which is linearly dependent on the state variables are considered.
It is shown that the mean square stability implies the exponential asymptotic stability with probability 1 and that it also implies the stability of the system without noise.
As a result, a sufficient condition of mean square stability is given. Using this result a sufficient condition is given for the stabilizability by a state feedback of a linear time-varying control system with state and control dependent noise.
