Stability analysis of linear stochastic neutral-type time-delay systems with two delays

This paper is concerned with stability analysis of stochastic neutral-type time-delay systems with two different delays in both the state variables and the retarded derivatives of state variables. Sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained by applying the Lyapunov-Krasovskii functional (LKF) based approach. A novel spectral radius based condition is imposed to guarantee the stability of the associated difference operator and a novel method is also proposed to analyze the stability of the overall system. Moreover, by carefully analyzing the relationship between these two different delays, a method is provided to construct all possible yet the minimal number of simple quadratic integral functions in the LKF, which helps to reduce both the conservatism and complexity of the resulting stability conditions. The effectiveness of the proposed approaches is illustrated by two numerical examples.