Exponential stability of a class of linear stochastic interconnected large-scale systems with time delay

The global exponential stability of a class of stochastic linear interconnected large-scale systems with time delay was analyzed based on M-matrix theory and box theory, by constructing a vector Lyapunov function. A criterion was concluded for global exponential stability of the systems by analyzing the stability of differential inequalities. It is obtained that a stochastic large-scale system with time delay is described as global exponential stable if the test matrix is an M-matrix, where the test matrix is constructed by employing the coefficient matrices of the system and the solutions of the Lyapunov equations which are interconnected with the system. The computation is convenient, so it is easy for application.