Robust exponential stability of a class of Markovian jump system with polytopic uncertainties and mode-dependent delays

The robust stability is investigated for a class of Markovian jump system with polytopic uncertainties and mode-dependent time-varying delays. In the Markovian jump system, the mode of delay is different from the mode of system. An appropriate parameter-dependent and mixed-mode-dependent Lyapunov-Krasovskii functional is constructed to reduce the conservatism. Based on the Lyapunov-Krasovskii theory, integral inequality and reciprocally convex approach, a sufficient condition in terms of linear matrix inequalities (LMIs) is derived, which ensures the system stable. The developed criterion is delay-dependent, mode-dependent as well as parameter-dependent. Finally, numerical examples are provided to illustrate the less conservatism of our results.