科研之友
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摘要
On the basis of the Lyapunov-Krasovskii method, the exponential stability in the mean square sense is investigated for Ito stochastic systems with Markovian switching and time-varying delay. The statistic properties of the Markov process and Brownian motion are employed to compute the constructed Lyapunov-Krasovskii functional of a rather general form. This enables us to make sense of the challenging problems in the stochastic framework, and then find a way to extend the techniques developed in the deterministic framework. Therefore, the stability conditions are established with the aid of some slack matrices and the boundary conditions on time-varying delay. Numerical examples are given to demonstrate the reduced conservatism.
