Robust stabilization of stochastic systems based on the LQ controller

Abstract

The robust exponential stability in mean square for a class of linear stochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we have designed an optimal controller which guarantees the exponential stability of the system. Actually, we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to have shown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria for the exponential stability on the linear stochastic uncertain closed-loop systems are given.