A semi-discretization method for delayed stochastic systems

Time delayed linear stochastic systems with state feedback is investigated. An extension of the semi-discretization method to stochastic systems is developed. Mappings of the second order moments are formulated by using the exact drift mapping and direct Itô integration. It is found that the exact drift mapping yields better results compared to the direct Itô integration. Stability boundaries and steady state second order moments are studied with the proposed method. The results are compared with the known exact solutions or the simulations. Good agreement among the results is found, which strongly validates the proposed method.