Aperiodic sampled-data control for local stabilization of memristive neural networks subject to actuator saturation: Discrete-time Lyapunov approach.

Abstract In this paper, the local stabilization of memristive neural networks (MNNs) with actuator saturation is investigated via aperiodic sampled-data control. Inspired by the characteristic of the control scheme, a novel sampling-interval-dependent Lyapunov functional (SIDLF) is constructed. The main contribution of the developed Lyapunov functional lies in that the requirement on its positive definiteness is replaced by a looped condition. Then, using some inequality techniques and the discrete-time Lyapunov approach, two sufficient criteria are derived to ensure the locally asymptotical stability of the trivial solutions of closed-loop systems. A unified work is developed that can deal with the presence of the saturation nonlinearity effects, aperiodic sampled-data control, as well as SIDLF. Additionally, two convex optimization schemes, aiming at enlarging the admissible initial region (AIR) and maximizing the upper bound of sampling interval, are respectively presented for designing the desired saturated sampled-data controller gains. A quantitative relationship between the maximum sampling interval and AIR is revealed. Finally, two numerical examples are given to illustrate the advantages and effectiveness of the derived theoretical conclusions.