On stability of neutral-type linear stochastic time-delay systems with three different delays

Abstract

We study in this paper the mean square exponential stability of neutral-type linear stochastic time-delay systems with three different delays by using the Lyapunov–Krasovskii functionals (LKFs) based approach. First, for a specified augmented state vector, a complete augmented LKF is constructed to contain all possible integrals so that its time-derivatives (understood in the deterministic sense) can be written as a linear function of the augmented vector. The redundant variables in the LKF are eliminated so as to reduce the computational burden. Moreover, the absolute value requirement of certain terms in the constructed LKFs are removed by analyzing carefully the complex relationship among these three different time delays. Then, for ten different cases of time delays, sufficient stability conditions in terms of linear matrix inequalities are obtained with the help of the Ito formula and properties of stochastic integrals. The degenerated cases that the delays satisfy some equalities are also discussed. A numerical example is employed to illustrate the effectiveness of the proposed approach.