Robust $H_{\infty }$ Control for Nonlinear Stochastic Systems: A Sliding-Mode Approach

This paper considers the sliding-mode control for nonlinear stochastic systems modeled by Ito stochastic differential equations. It is noted that there exist state and exogenous disturbance-dependent noise in the controlled systems. By utilizing H _infin disturbance attenuation technique, a novel sliding-mode control method is proposed such that the resultant system is asymptotically stable in probability with a prescribed H _infin performance. Sufficient conditions for the solvability of these problems are derived via nonlinear Hamilton-Jacobi (HJ)-type inequalities. Moreover, it is shown that for a class of special nonlinear stochastic systems, the H _infin-sliding-mode control design can be obtained by solving linear matrix inequalities (LMIs). Finally, a numerical simulation example is given.