State Feedback H_∞ Control for a Class of Nonlinear Stochastic Systems

This paper discusses the H∞ control problem for a class of nonlinear stochastic systems with both state- and disturbance-dependent noise. By means of Hamilton--Jacobi equations, both infinite and finite horizon nonlinear stochastic H_∞ control designs are developed. Some results on nonlinear H_∞ control of deterministic systems are generalized to a stochastic setting. We introduce some useful concepts such as "zero-state observability" and "zero-state detectability" which, together with the stochastic LaSalle invariance principle, yield some valuable consequences in infinite horizon nonlinear stochastic H_∞ control.