An improved result on synchronization control for memristive neural networks with inertial terms and reaction-diffusion items

Stability and pinning synchronization of delayed memristive neural networks with fractional-order and reaction-diffusion terms

Global asymptotic stability and synchronization are explored in this paper for fractional delayed memristive neural networks with reaction-diffusion terms (FDRDMNNs) in sense of Riemann-Liouville. First, we introduce diffusion into the existing model of fractional delayed memristive neural networks. Next, in terms of Green's theorem and inequality technique, a less conservative criterion for the asymptotic stability of FDRDMNNs is given by endowing Lyapunov direct method. Then, the appropriate pinning feedback controllers and adaptive controllers are designed to achieve the synchronization of the FDRDMNNs, and two sufficient conditions for global asymptotic synchronization are acquired. In addition, the results based on algebraic inequalities enhance some existing ones. The numerical simulations finally verify the validity of the derived results.

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

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.

Gain-Scheduled Finite-Time Synchronization for Reaction-Diffusion Memristive Neural Networks Subject to Inconsistent Markov Chains

An innovative class of drive-response systems that are composed of Markovian reaction-diffusion memristive neural networks, where the drive and response systems follow inconsistent Markov chains, is proposed in this article. For this kind of nonlinear parameter-varying systems, a suitable gain-scheduled controller that involves a mode and memristor-dependent item is designed, so that the error system is bounded within a finite-time interval. Moreover, by constructing a novel Lyapunov-Krasovskii functional and employing the canonical Bessel-Legendre inequality and free-weighting matrix method, the conservatism of the finite-time synchronization criterion can be greatly reduced. Finally, two numerical examples are provided to illustrate the feasibility and practicability of the obtained results.