Synchronization of memristive delayed neural networks via hybrid impulsive control

Zhang

Discrete Dynamics in Nature and Society

2019

This paper is concerned with the mean-square exponential input-to-state stability problem for a class of stochastic Cohen-Grossberg neural networks. Different from prior works, neutral terms and mixed delays are discussed in our system. By employing the Lyapunov-Krasovskii functional method, Itô formula, Dynkin formula, and stochastic analysis theory, we obtain some novel sufficient conditions to ensure that the addressed system is mean-square exponentially input-to-state stable. Moreover, two numerical examples and their simulations are given to illustrate the correctness of the theoretical results.

Section: Introductionmentioning

confidence: 99%

“…Based onAssumptions 2,3,4,5,6, and 13, the trivial solution of system(24) is mean-square exponentially input-to-state stable, if there exist positive constants , , V , ( = 1, 2, . .…”

mentioning

confidence: 99%

Analysis of Exponential Stability for Neutral Stochastic Cohen-Grossberg Neural Networks with Mixed Delays

Zhang

Discrete Dynamics in Nature and Society

2019

“…Besides, it only requires small control gains and acts at certain discrete instants, thereby reducing the amount of transmitted information and control costs [14]. Considering the advantages of the impulsive control strategy, the issue of impulsive synchronization of MNNs has been wildly studied [15][16][17][18][19]. In [15], by utilizing the distributed impulsive control method, the synchronization problem for a class of MNNs with stochastic disturbance has been extensively studied.…”

Section: Introductionmentioning

confidence: 99%

Event-triggered hybrid impulsive control for synchronization of memristive neural networks

Zhang

Bao

2020

Sci. China Inf. Sci.

This paper is concerned with the complete synchronization of memristive neural networks (MNNs) with time-varying delays. An event-triggered hybrid state feedback and impulsive controller is designed to save the limited system communication resources, and parameter mismatch is considered in the control design process. Based on the Lyapunov functional approach and the comparison principle for impulsive systems, a sufficient synchronization criterion is developed to derive the master MNN and response MNN. Additionally, under the event-triggered mechanism there exists a positive lower bound for inter-execution time, which implies the avoidance of Zeno behavior. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed synchronization design methods.

Mathematical Biosciences &Amp; Engineering

“…Since time delays often appear in engineering, biological and economical systems, and sometimes they may poorly affect the performance of a system. The problem of stability of IDSs and impulsive stabilization of delay systems have been extensively investigated [119,108,104,96,36,98,18,24]. For example, [104] studied the stability of a class of nonlinear impulsive switching systems with time-varying delays.…”

mentioning

confidence: 99%

“…Based on the common Lyapunov function method and Razumikhin technique, several stability criteria are established for nonlinear impulsive switching systems with time-varying delays. In [98], by structuring hybrid impulsive and feedback controllers, synchronization problem of the memristive delayed neural networks is proposed. Then, based on differential inclusions, several synchronization criteria for the memristive delayed neural networks are obtained by impulsive control theories, special inequalities and the Lyapunov-type functional.…”

mentioning

confidence: 99%

Review of stability and stabilization for impulsive delayed systems

Xiao

Li²,

Xi³

et al. 2018

167

This paper reviews some recent works on impulsive delayed systems (IDSs). The prime focus is the fundamental results and recent progress in theory and applications. After reviewing the relative literatures, this paper provides a comprehensive and intuitive overview of IDSs. Five aspects of IDSs are surveyed including basic theory, stability analysis, impulsive control, impulsive perturbation, and delayed impulses. Then the research prospect is given, which provides a reference for further study of IDSs theory.