Delay-probability-distribution-dependent robust stability analysis for a class of stochastic system with time-varying delay

The delay-probability-distribution-dependent robust stability problem for a class of uncertain stochastic system with time-varying delay is investigated. The information of probability distribution of the time delay is considered and transformed into parameter matrices of the transferred stochastic model. Based on the Lyapunov--Krasovskii functional and stochastic stability theory , a delay-probability-distribution-dependent sufficient condition is obtained by the form of the linear matrix inequality (LMI) format such that delayed stochastic systems are robustly globally asymptotically stable in the mean-square sense for all admissible uncertainties. Finally, numerical examples are given to illustrate the effectiveness and less conservativeness of the proposed method.