This paper investigates the problem of robust stabilization for switched non-linear systems with time-varying delays under asynchronous switching. Sufficient conditions for the existence of the robust stabilization problem are developed. First, when the switching instants of the controller experience delays with respect to those of the system, a state feedback controller is proposed to guarantee exponential stability for switched systems with time-varying delays. The dwell-time approach and free weighting matrix scheme are utilized for stability analysis and controller design. Then the approach is extended to take into account switched time-delay systems with Lipschitz non-linearities and structured uncertainties. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
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