Robust H∞ control for nonlinear stochastic systems: A sliding-mode approach

This paper considers the sliding-mode control for nonlinear stochastic systems modeled by Itô stochastic differential equations. It is noted that there exist state and exogenous disturbance-dependent noise in the controlled systems. By utilizing H_∞ 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_∞ 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_∞ -sliding-mode control design can be obtained by solving linear matrix inequalities (LMIs). Finally, a numerical simulation example is given. © 2008 IEEE.