Abstract
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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> disturbance attenuation technique, a novel sliding-mode control method is proposed such that the resultant system is asymptotically stable in probability with a prescribed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> -sliding-mode control design can be obtained by solving linear matrix inequalities (LMIs). Finally, a numerical simulation example is given.
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