H∞ control for a class of stochastic switched nonlinear systems: An average dwell time method

Abstract In this paper, we investigate the H ∞ control problem for a class of stochastic switched nonlinear systems by employing an average dwell time approach. First, we present when all subsystems are global asymptotically stable in the mean (GASiM), the stochastic switched system under an average dwell time scheme is GASiM and possesses a weighted L 2 -gain. Then we extend this result to the case where both GASiM subsystems and unstable subsystems coexist, by showing that apart from the average dwell time scheme, if the activation time ratio between GASiM subsystems and unstable ones is not less than a specified constant, sufficient conditions for the weighted H ∞ performance of the switched system are guaranteed. Finally, a simulation example is provided to illustrate the validity of the developed results.

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