Sanbo Ding

Exponential Stability and Stabilization of Delayed Memristive Neural Networks Based on Quadratic Convex Combination Method

This paper is concerned with the exponential stability and stabilization of memristive neural networks (MNNs) with delays. First, we present some generalized double-integral inequalities, which include some existing inequalities as their special cases. Second, combining with quadratic convex combination method, these double-integral inequalities are employed to formulate a delay-dependent stability condition for MNNs with delays. Third, a state-dependent switching control law is obtained for MNNs with delays based on the proposed stability conditions. The desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities. Finally, the feasibility and effectiveness of the proposed results are tested by two numerical examples.

Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays

As an indispensable part of memristive synaptic weights, the switching jumps can induce instability, oscillation or even chaos to the memristive network system. Based on the available information of the switching jumps, this paper is concerned with the stochastic exponential synchronization of a class of memristive neural networks with multiple time-varying delays. By using stochastic differential inclusions and Lyapunov stability theory, discontinuous state feedback controller which depends upon the switching jumps is proposed. Compared with the previous state feedback scheme, more information of memristive synaptic weights is used to design the synchronous controller which ensures the stochastic exponential synchronization of considered networks. When the information of switching jumps is incomplete, discontinuous adaptive controller which is independent of the switching jumps is also designed, thus the applicability of synchronization is broadened. A numerical example is provided to illustrate the effectiveness and potential of the proposed design techniques.

Stability of Recurrent Neural Networks With Time-Varying Delay via Flexible Terminal Method

This brief is concerned with the stability criteria for recurrent neural networks with time-varying delay. First, based on convex combination technique, a delay interval with fixed terminals is changed into the one with flexible terminals, which is called flexible terminal method (FTM). Second, based on the FTM, a novel Lyapunov–Krasovskii functional is constructed, in which the integral interval associated with delayed variables is not fixed. Thus, the FTM can achieve the same effect as that of delay-partitioning method, while their implementary ways are different. Guided by FTM, Wirtinger-based integral inequality and free-weight matrix method are employed to develop several stability criteria, respectively. Finally, the feasibility and the effectiveness of the proposed results are tested by two numerical examples.

Novel Switching Jumps Dependent Exponential Synchronization Criteria for Memristor-Based Neural Networks

This paper investigates the problem of global exponential synchronization for memristor-based neural networks with delay. Based on the nonsmooth analysis and differential inclusion theory, a new analytic technique is employed to design a discontinuous state feedback controller, which ensures the memristor-based drive system exponential synchronize with the response system. The succinct synchronization conditions is closely relate to the switching jumps. The estimated rate of the exponential synchronization can be obtained by solving a sample algebra equation. Simulation results are given to show the effectiveness and benefits of the proposed methods.

Stability criterion for delayed neural networks via Wirtinger-based multiple integral inequality

This brief provides an alternative way to reduce the conservativeness of the stability criterion for neural networks (NNs) with time-varying delays. The core is that a series of multiple integral terms are considered as a part of the Lyapunov-Krasovskii functional (LKF). In order to estimate the multiple integral terms in the derivative of the LKF, a multiple integral inequality, named Wirtinger-based multiple integral inequality (WMII), is proposed. This inequality includes some recent related results as its special cases. Based on the multiple integral forms of LKF and the WMII, a novel delay dependent stability criterion for NNs with time-varying delays is derived. The effectiveness of the established stability criterion is verified by an open example.

Dissipativity Analysis for Stochastic Memristive Neural Networks With Time-Varying Delays: A Discrete-Time Case

In this paper, the dissipativity problem of discrete-time memristive neural networks (DMNNs) with time-varying delays and stochastic perturbation is investigated. A class of logical switched functions are put forward to reflect the memristor-based switched property of connection weights, and the DMNNs are then recast into a tractable model. Based on the tractable model, the robust analysis method and Refined Jensen-based inequalities are applied to establish some sufficient conditions that ensure the

Wirtinger-based multiple integral inequality for stability of time-delay systems

(\mathcal {Q},\mathcal {S},\mathcal {R})-\gamma -\text {disspativity}

Hierarchy of stability criterion for time-delay systems based on multiple integral approach

of DMNNs. Two numerical examples are presented to illustrate the effectiveness of the obtained results.

Stop and Go adaptive strategy for synchronization of delayed memristive recurrent neural networks with unknown synaptic weights

ABSTRACT Note that the conservatism of the delay-dependent stability criteria can be reduced by increasing the integral terms in Lyapunov–Krasovskii functional (LKF). This brief revisits the stability problem for a class of linear time-delay systems via multiple integral approach. The novelty of this brief lies in that a Wirtinger-based multiple integral inequality is employed to estimate the derivative of a class of LKF with multiple integral terms. Based on these innovations, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. Two numerical examples are exploited to demonstrate the effectiveness and superiority of the proposed method.

Leader–follower consensus of multi-agent systems in directed networks with actuator faults

Taking a class of time-delay systems as research object, this brief aims at developing a theoretical support on the hierarchy of stability criterion which is derived by the multiple integral approach and free-weighting matrix technique. The hierarchy implies that the conservatism of stability criterion can be reduced by increasing the ply of integral terms in Lyapunov–Krasovskii functional (LKF). Together with three numerical experiments, the hierarchy of stability criterion is further shown.