Abstract
The paper develops the robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control to deal with the uncertain stochastic nonlinear systems driven by noise of unknown covariance. By introducing the notion of stochastic dissipation, we point out that the stochastic dissipative system has the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> gain property. From this point, we solve the robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control problem for the uncertain stochastic nonlinear systems with noise of unknown covariance via state feedback. Furthermore, we provide the sufficient conditions under which the dynamic output controller is obtained to handle the robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> problem for such stochastic nonlinear systems on the basis of the solvability of the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control problem by state feedback.
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