LMI-based criterion on stochastic ISS property of delayed high-order neural networks with explicit gain functions and simply event-triggered mechanism

Abstract In this paper, by transforming the high-order system into the system with vector-matrix form, the authors employed variational methods in Sobolev spaces, Lyapunov function method, Dynkin’s formula and comparison principle to deduce the stochastic input-to-state stability in mean square on the high-order time-delays reaction-diffusion neural networks under the concise event-triggered mechanism. Remarkably, it is the first paper in which the LMI-based criterion of input-to-state stability of time-delays high-order reaction-diffusion neural networks with event-triggered control is derived, in which the diffusion item plays its role. Not similarly as those of previous literature, the sufficient conditions of the main result in this paper are not involved to Lyapunov function, which implies that the conditions of this paper is easier to be verified than ever. With the help of computer Matlab LMI toolbox, a numerical example illustrates the effectiveness of proposed methods.