A Class Of Stochastic Delay System Stability Studies

Time delays and uncertain parameters frequently occur in many practical sys-tems, which makes the system analysis more complicated and di?cult, and becomesusually major causes of instability. Therefore, the study about systems with timedelays is important in both theory and practice.This paper investigates the problem of exponential mean square (robust) sta-bility for a class of continuous-time linear uncertain systems with state delay whichhas probability characteristics. Based on a new probability distribution of the statedelays, the original system model is transformed to one with stochastic coe?cientmatrices. By constructing an appropriate Lyapunov-Krasovskii functional and usingthe linear matrix inequality technique, the exponential mean square stability criteriaare derived. It is also shown that both the EMSS criterion in [Int. J. Robust Non-linear Control, 2009, 19(4), 377-393] and a special case of the EMSS criterion givenin this paper have the same solvability, which implies that our EMSS criteria areless conservative. The EMSS criteria given in this paper remove any free weightingmatrix in [1], which reduces the computational complexity, and also indicates thatthe conservativeness of the EMSS criteria will not be weaker when the number offree weighting matrices increases.Numerical examples and simulations are given to demonstrate the e?ectivenessand superiority of the proposed method.