Weighted pseudo θ-almost periodic sequence solution and guaranteed cost control for discrete-time and discrete-space stochastic inertial neural networks

This article considers the dual hybrid influences of both discrete spatial diffusions and discrete time in a stochastic inertial neural networks via the methods of exponential Euler difference and second order central finite difference. Based on a non-decomposed constant variation formula, and the theories of semi-flow and metric dynamical systems, the existence of a unique weighted pseudo θ-almost periodic sequence solution is addressed to the discrete space and time stochastic inertial neural networks. Further, a guaranteed cost controller is designed to complete a global exponential stabilization for this discrete networks by establishing a framework of drive, response and error networks. Meanwhile, global exponential stability in the sense of mean square is achieved as well. This discussion is pioneering in considering discrete spatial diffusions in inertial neural networks and offers the studying bases for future researches.