Improved delay-dependent stability criterion and controller design for stochastic systems with time delays

This paper investigates the stability and stabilization problems of stochastic systems with time delays. By using a delay decomposition approach, a novel Lyapunov-Krasovskii functional is proposed. Combining with the Itô formula and some tighter bounding technologies, a new delay-dependent stability criterion for linear delayed stochastic systems is derived in terms of linear matrix inequalities. Employing the obtained result, a state feedback controller is constructed to ensure the stability in mean square of the corresponding closed-loop system. A numerical example is given to verify the effectiveness of the design method.