Exponential stability of discrete-time delayed neural networks with saturated impulsive control

This paper examines the problem of the locally exponentially stability for impulsive discrete-time delayed neural networks (IDDNNs) with actuator saturation. By fully considering the delay information of the state of the considered system, a new delay-dependent polytopic representation within a discrete-time framework is obtained. Based on the delay-independent polytopic representation approach, the saturation term is expressed as a delay-dependent convex combination. In order to obtain some less conservative stability conditions and estimate a larger of the domain of attraction, a novel type of Lyapunov-Krasovskii function (LKF) dependent on the delay information and the impulses instant is proposed, which is called time-dependent LKF. Then, by combining with the proposed LKF, a discrete Wirtinger-based inequality, an extended reciprocally convex matrix inequality and some novel analysis techniques, several new exponential stability criteria dependent on the bounds of the delay are presented. Moreover, when saturation constraints are not considered in the impulsive controller, the stability of the system is also discussed. Finally, two examples are given to confirm the applicability of the proposed results.