On the stability and mean square stabilization of a class of linear stochastic systems controlled by impulses

This paper is devoted to the analysis of the mean-square stability of a class of linear time-varying impulsive Ito-type stochastic systems. We succeed to obtain necessary and sufficient stability conditions in the general time-varying case. This result is obtained thanks to the theory of positive operators on Hilbert spaces. The problem of state­feedback stabilization is treated as well.