The problem of robust stabilization of uncertain, stochastic, switched non-linear systems under asynchronous switching is investigated in the current paper, where asynchronous switching means that switching of the controllers has a lag to the switching of system modes. The parameter uncertainties are allowed to be norm bounded and enter into the state matrix. The purpose of this problem is to design a state feedback controller such that, for all admissible uncertainties, the resulting closed-loop system is exponentially stable in the mean square sense. By using the average dwell-time approach and stochastic analysis techniques, sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of a set of matrix inequalities. A numerical example is exploited to show the usefulness of the results obtained.
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