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

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3 Author(s)
Yugang Niu ; Sch. of Inf. Sci. & Eng., East China Univ. of Sci. & Technol., Shanghai ; Ho, D.W.C. ; Xingyu Wang

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.

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Automatic Control, IEEE Transactions on  (Volume:53 ,  Issue: 7 )