Stabilization in probability of nonlinear stochastic systems with guaranteed cost

We deal with nonlinear dynamical systems, consisting of a linear nominal part plus model uncertainties, nonlinearities, and both additive and multiplicative random noise, modeled as a Wiener process. In particular, we study the problem of finding suitable measurement feedback control laws such that the resulting closed-loop system is stable in some probabilistic sense and a given cost functional is minimized. We give a Lyapunov-based separation result which splits the control design into a state feedback problem and a filtering problem. Finally, we point out constructive algorithms for solving the state feedback and filtering problems with arbitrarily large region of attraction for a wide class of nonlinear systems, which at least include feedback linearizable systems.