A new delay-distribution-dependent robust stability criterion for uncertain systems with time-varying delay

This paper investigates the problem of robust stability for a class of continuous-time linear uncertain systems with time-delay state delay which has probability characteristics. By using the information of delay-distribution and constructing an appropriate Lyapunov-Krasovskii functional, a robust Exponential Mean Square Stability (EMSS) criterion of systems is derived. The criterion given by this paper does not need to bring in any free weighting matrices, which reduces the computational complexity, and it also indicates that the conservativeness of the robust EMSS criterion will not be weaker when the number of free weighting matrices increases. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.