A problem of feedback stabilization of hybrid systems with time-varying delay and Markovian switching is considered. Sufficient conditions for stability based on linear matrix inequalities (LMIs) for stochastic asymptotic stability is obtained. The stability result depended on the mode of the system and of delay-independent. The robustness results of such stability concept against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results.

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A problem of feedback stabilization of hybrid systems with time-varying delay and Markovian switching is considered. Delay-dependent sufficient conditions for stability based on linear matrix inequalities (LMI's) for stochastic asymptotic stability is obtained. The stability result depended on the mode of the system and of delay-dependent. The robustness results of such stability concept against all admissible uncertainties are also investigated. This new delay-dependent stability criteria is less conservative than the existing delay-independent stability conditions. An example is given to demonstrate the obtained results.

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