State Feedback $H_\infty$ Control for a Class of Nonlinear Stochastic Systems

Authors:
Weihai Zhang;Bor-Sen Chen
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2006

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Abstract

This paper discusses the $H_{\infty}$ 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 $H_\infty$ control designs are developed.Some results on nonlinear $H_\infty$ 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 $H_\infty$ control.