Delay-partition and delay-distribution based Exponential Mean Square Stability criteria for continuous-time linear systems with state delay

This paper presents Exponential Mean Square Stability (EMSS) criteria of a class of continuous-time linear systems with state delay which has probability characteristics. By comprehensively using the information of delay-partition and delay-distribution, and constructing an appropriate Lyapunov-Krasovskii functional, EMSS criteria in the form of linear matrix inequalities are obtained. Compared with existing results, the EMSS criteria provided in this paper have three advantages: (i) a time-delay model submitting to multinomial distribution is first introduced, and thus the information of delay-partition and delay-distribution is sufficiently used; (ii) the EMSS criteria given by this paper may be less conservative; and (iii) the EMSS criteria given by this paper does not need to bring in any free weighting matrix, which reduces the computational complexity. These advantages indicate that the conservativeness of the EMSS criteria will not be weaker when the number of free weighting matrices increases. Finally, a numerical example is given to demonstrate the effectiveness and superiority of the proposed method.