Moment equations of linear Itô stochastic systems with applications

In this paper, with the Kronecker's product and Kronecker's sum of matrices, the 2nd order moment equations of linear Itô stochastic systems are dervided. Based On the moment equations obtained, a necessary and sufficient condition for the mean-square asymptotic stability of linear Itô stochastic systems is obtained. For the time-invariant stochastic systems, the necessary and sufficient condition is just the same as the Hurwitz property of certain matrices related to the coefficient matrices of the systems. An algorithm STILSS is given for testing the mean-square asymptotic stability of time-invariant linear Itô stochastic systems.