H∞ control of stochastic nonlinear systems with dynamic uncertainties

This paper extends H_infin control theory to a more general class of stochastic nonlinear systems with dynamic uncertainties. From the view of stochastic dissipation, we investigate the L₂ robust performance rule design for this general class of systems. Under some mild assumptions on the unmodeled dynamics, we establish the relationship between the L₂ gain of the dynamic uncertain stochastic nonlinear systems and the solution to a certain HJI inequality. Furthermore, for some systems satisfying some proper matching conditions, we discuss the methods of acquiring the control laws without solving HJI inequality.