Stability of Inertial Neural Network with Time-Varying Delays Via Sampled-Data Control

Abstract

In this paper, the stability problem is studied for inertial neural network with time-varying delays. The sampled-data control method is employed for the system design. First, by choosing a proper variable substitution, the original system is transformed into first-order differential equations. Then, an input delay approach is applied to deal with the stability of sampling system. Based on the Lyapunov function method, several sufficient conditions are derived to guarantee the global stability of the equilibrium. Furthermore, when employing an error-feedback control term to the slave neural network, parallel criteria regarding to the synchronization of the master neural network are also generated. Finally, some examples are given to illustrate the theoretical results.

Stability analysis of inertial neural networks: A case of almost anti‐periodic environment

“…The model investigated in this paper is a natural generalization of the models studied in the previous papers. 12,15,16,22,23 Besides, our inertial neural networks model is analyzed in the almost anti-periodic environment which is a natural generalization of anti-periodic space considered in previous studies.…”

“…The neural networks systems with delays have attracted the interest of many researchers and some excellent results are reported. For stability, the papers of Li et al and Wang and Tian 15,16 realize the asymptotic stability, and Zhang and Cao 17 proved the stability in finite time of a class of inertial neural networks with time delays with constant coefficients. To guarantee the existence of the solutions, previous studies 14,18,19 resort to periodic and anti-periodic solutions.…”

Finite-Time $\mathcal {L}_{2}$-$\mathcal {L}_{\infty }$ Synchronization for Semi-Markov Jump Inertial Neural Networks Using Sampled Data

“…In [35], the issue of Heterogeneous time-varying delays was concerned for the synchronization of the INNs. The stability of the INNs was studied via sampled-data control in [36]. Regretfully, the analysis of L 2 -L ∞ performance index is rarely adopted for the SMJINNs in the existing literature, not to mention that take the sampled-data control into account.…”

Non-fragile quasi-synchronization of delayed heterogeneous dynamical networks with memory sampled-data control

“…Thus, the synchronization problem of complex dynamical networks with time delay has raised considerable concern in recent years. In fact, the sampled-data control for complex networks with time delay have been reported in Lu et al (2020); Wang and Tian (2019); Wang et al (2020); Liu and Su, (2019); and Que et al (2019). Lu et al (2020) studied the H ∞ output synchronization of the directed coupled reaction-diffusion neural networks with mixed delays.…”

“…Lu et al (2020) studied the H ∞ output synchronization of the directed coupled reaction-diffusion neural networks with mixed delays. Wang and Tian (2019) studied the problem of stability of inertial neural network with time-varying delays under sampled-data control. In order to deal with the stability of sampling system, the input delay method is proposed.…”