Aperiodic Sampled-Data Control for Stabilization of Memristive Neural Networks With Actuator Saturation: A Dynamic Partitioning Method

This article is concerned with the local stabilization of memristive neural networks subject to actuator saturation via aperiodic sampled-data control. A dynamic partitioning point is elegantly introduced, which is placed between the latest sampling instant and the present time to utilize more information of the inner sampling. To analyze the stability of the closed-loop system, a time-dependent two-side looped functional, which fully utilizes the state information on the entire sampling interval as well as at the dynamic partitioning point, is constructed. It relaxes the positive definiteness of traditional Lyapunov functional inside the sampling interval and therefore, provides the possibility to derive less conservative stability results. Besides, an auxiliary system is established to describe the dynamics at the partitioning point. On the basis of the constructed looped functional, the discrete-time Lyapunov theorem, and some estimation approaches, a linear matrix inequalities-based stability criterion is developed, and then, the sampled-data saturated controller is designed to ensure the local asymptotic stability of the closed-loop system. Thereafter, two optimization problems are developed to seek the desired feedback gain and to expand the estimation of the region of attraction or to enlarge the upper bound of the sampling interval. Eventually, a numerical example is given to demonstrate the effectiveness and the superiority of the proposed results.