Robust delay-probability-distribution stability of linear stochastic systems with time-varying delay

This paper is concerned with the robust stability of a class of linear uncertain stochastic systems with nonlinear time-varying stochastic time-delay which is characterized by a Bernoulli stochastic process with given distribution probability in a given variation range. By constructing a new Lyapunov-Krasovskii functional, we derive for the system the sufficient conditions of mean-square exponential stability in terms of the linear matrix inequalities(LMIs), which can be checked readily by using MATLAB toolbox. The feature of our results is the conclusion of stability conditions being dependent not only on the probability distribution of the time-delay, but also on the upper bound of the its derivative. Meanwhile, we also show that the allowable variation range of the time-varying stochastic time-delay can be greater than that of a deterministic time-delay in ensuring the same stability; this demonstrates the less conservativeness of our requirements than the traditional ones. An example is given to illustrate the effectiveness of the proposed method.