Refined exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delays

This paper is concerned with exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delay. By combining Lyapunov-Krasovskii functional method and Jensen inequality technique, a delay-dependent and delay-rate-dependent exponential stability criterion for stochastic Markovian jump systems with nonlinearity and time-varying delay is investigated. The proposed approach removes some free-weighting matrices required in [Int. J. Robust Nonlinear control, 2010, 20(1): 16-26], which reduces computational complexity. It is mathematically shown that the approach proposed here may be less conservative than the one mentioned above. Two numerical examples are provided to illustrate the applicability and the benefits of the proposed approach.