Class Of Memristor-based Neural Networks Research Articles

Intermittent Exponential Synchronization for Memristor-Based Neural Networks With Inertial Items and Mixed Time-Varying Delays

This article investigates the exponential synchronization problem for a class of memristor-based neural networks with mixed time-varying delays and parameter perturbations, and inertial items are considered (MINNs). A periodically intermittent control protocol is designed to guarantee the exponential synchronization between two MINNs. Then, by adopting nonsmooth analysis, Halanay inequality, and Lyapunov theory, the exponential synchronization criteria for MINNs under the proposed controller are obtained. Furthermore, instead of the reduced-order method, the synchronization of MINNs is considered under the framework of the second-order system directly, which is different from existing literature. Some numerical simulations are presented to show the validity of the proposed criteria in the end.

Bounded real lemmas and exponential [formula omitted] control for memristor-based neural networks with unbounded time-varying delays

This paper focuses on developing a bounded real lemma (BRL) and designing a state-feedback controller which guarantees a prescribed H∞ performance level for a class of memristor-based neural networks (MNNs) with unbounded time-varying delays. Firstly, a BRL for MNNs is presented by taking a new approach based on system solutions. This approach requires neither transformation of the model nor construction of Lyapunov–Krasovskii functionals, thereby reducing computational effort and complexity. In addition, the obtained BRL contains only a few simple inequalities, which can be easily solved by using MATLAB. Secondly, the condition for the existence of exponential H∞ controller is given based on the obtained BRL. Finally, two simulation examples demonstrate the validity of the theoretical results.

A Representation of System Solutions for Global Exponential Stabilization of Memristor-Based Neural Networks With Unbounded Time-Varying Delays

This article mainly discusses the global exponential stabilization of a class of memristor-based neural networks (MNNs) with unbounded time-varying delays. In this article, a new approach without constructing any Lyapunov–Krasovskii functional is proposed to derive the global exponential stabilization criterion containing only a few simple inequalities. This approach is based on the representation of the system solution, which can derive simpler criteria than the existing approaches. In addition, this approach does not limit the range of the derivative of the unbounded time-varying delay, which implies that the stabilization criterion obtained is weaker conservative. Finally, two numerical examples are employed to demonstrate the effectiveness of the approach.

Fixed-Time Lag Synchronization Analysis for Delayed Memristor-Based Neural Networks

In this paper, the fixed-time lag synchronization for a general class of memristor-based neural networks (MNNs) with time delays is considered. Under the extended Filippov-framework theory, some sufficient criteria for fixed-time lag synchronization of delayed MNNs are derived based on the Lyapunov function. Besides, two types of controllers are given to ensure the fixed-time lag synchronization of the corresponding system, while the settling time of synchronization are also estimated. Finally, a numerical example is given to demonstrate the effectiveness of the developed method and the theoretical results.

Fixed-time synchronization of the impulsive memristor-based neural networks

This paper concerns the fixed-time synchronization of a class of memristor-based neural networks with impulsive effects. Since impulses may destroy the synchronization, it is indispensable to design suitable controllers to control its unpredictable effects. In the present paper, two control schemes are proposed to achieve fixed-time synchronization of the impulsive memristor-based neural networks. Finally, two examples and their numerical simulations are presented to show the effectiveness of the theoretical results.

Synchronization of Memristor-Based Delayed Neural Networks via Aperiodically Intermittent Control

This paper investigates the exponential synchronization problem for a class of memristor-based neural networks via novel aperiodically intermittent control approach. By using Lyapunov stability theory, several novel and useful synchronization criteria are obtained, which guarantee global exponential synchronization of memristive neural networks. Finally, a numerical example is given to illustrate the effectiveness of proposed method.

Reachable Set Estimation for a Class of Memristor-Based Neural Networks With Time-Varying Delays

This paper investigates the reachable set estimation problem for a class of memristor-based neural networks with time-varying delays and bounded disturbances. By constructing a Lyapunov–Krasovskii functional, a sufficient condition for the solvability of the addressed problem is established based on linear matrix inequality. This condition ensuring the existence of an ellipsoid that contains all the states under initial conditions. A stability criterion of memristor-based neural networks with time-varying delays is also given. Two numerical examples are provided to show the effectiveness of the proposed methods.

Delay-Dependent Passivity and Stability Analysis for a Class of Memristor-Based Neural Networks with Time Delay in the Leakage Term

This paper is concerned with the problem of passivity and stability analysis for a class of memristor-based neural networks with leakage delay and state-dependent switched memductance functions. By combining differential inclusions with set-valued maps and constructing a proper Lyapunov–Krasovskii functional, delay-dependent criteria in terms of linear matrix inequalities are obtained for the passivity of the memristive neural networks. Meanwhile, based on the derived criteria, stability criteria are obtained for the networks via Barbalat’s lemma. Finally, a numerical example is given to illustrate the feasibility of the theoretical results.

Passivity analysis and state estimation for a class of memristor-based neural networks with multiple proportional delays

This paper is concerned with the problem of a passivity analysis for a class of memristor-based neural networks with multiple proportional delays and the state estimator is designed for the memristive system through the available output measurements. By constructing a proper Lyapunov-Krasovskii functional, new criteria are obtained for the passivity and state estimation of the memristive neural networks. Finally, a numerical example is given to illustrate the feasibility of the theoretical results.

Exponential Stability of Almost Periodic Solutions for Memristor-Based Neural Networks with Distributed Leakage Delays.

In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).

Exponential lag synchronization for memristor-based neural networks with mixed time delays via hybrid switching control

In this paper, the exponential lag synchronization for a class of memristor-based neural networks with mixed time-delays is investigated via hybrid switching control method. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the exponential lag synchronization of memristor-based chaotic neural networks are obtained by designing two diffident hybrid switching controllers and constructing novel Lyapunov functionals. Finally, a numerical example with simulation is given to show the effectiveness and feasibility of the obtained results.

Finite-time stabilization control of memristor-based neural networks

This paper investigates the finite-time stabilization problem for a general class of memristor-based neural networks (MNNs). Firstly, based on set-valued analysis and Kakutani’s fixed point theorem of set-valued maps, the existence of equilibrium point can be guaranteed for MNNs. Then, by designing novel discontinuous controller, some sufficient conditions are proposed to stabilize the states of such MNNs in finite time. Moreover, we give the upper bound of the settling time for stabilization which depends on the system parameters and control gains. The main tools to be used involve the framework of Filippov differential inclusions, non-smooth analysis, matrix theory and the famous finite-time stability theorem of nonlinear system. Finally, the theoretical results are verified by concrete examples with computer simulations.

Adaptive anti-synchronization and [formula omitted] anti-synchronization for memristive neural networks with mixed time delays and reaction–diffusion terms

This paper firstly treats of the anti-synchronization of a class of memristor-based neural networks with mixed time delays and reaction–diffusion terms. An adaptive controller is designed such that the response system can be synchronized with the drive system by utilizing Lyapunov stability theory. Furthermore, the synchronization criteria derived in this paper are associated with the time switching. In addition, the H∞ anti-synchronization of memristive neural networks has been studied as well. Therefore, the results obtained in this paper are more general and extend the previous work. Finally, two numerical examples and their simulations are given to show the effectiveness of the obtained results.

Finite-time synchronization for memristor-based neural networks with time-varying delays

Memristive network exhibits state-dependent switching behaviors due to the physical properties of memristor, which is an ideal tool to mimic the functionalities of the human brain. In this paper, finite-time synchronization is considered for a class of memristor-based neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the finite-time synchronization of memristor-based chaotic neural networks are obtained by using analysis technique, finite time stability theorem and adding a suitable feedback controller. Besides, the upper bounds of the settling time of synchronization are estimated. Finally, a numerical example is given to show the effectiveness and feasibility of the obtained results.

Periodicity and dissipativity for memristor-based mixed time-varying delayed neural networks via differential inclusions

In this paper, we investigate a class of memristor-based neural networks with general mixed delays involving both time-varying delays and distributed delays. By using the Mawhin-like coincidence theorem, together with the differential inclusion theory, M-matrix properties and differential inequality techniques, some novel criteria are established for ensuring the periodicity and dissipativity for the addressed neural networks. Finally, two numerical examples with simulations are presented to demonstrate the effectiveness of the theoretical results.

State estimation for memristor-based neural networks with time-varying delays

This paper is concerned with the state estimation problem for a class of memristor-based neural networks with time-varying delay. A delay dependent condition is developed to estimate the neuron states through observed output measurements such that the error system is globally asymptotically stable. By constructing more effective Lyapunov functionals, and combining with Jensen integral inequality and free-weighting matrix approach, a less conservative sufficient condition for the existence of state estimator is formulated in terms of linear matrix inequality, which can be checked efficiently by using some standard numerical packages. Finally, a numerical example is given to demonstrate the effectiveness of the presented results.

On the periodic dynamics of memristor-based neural networks with time-varying delays

In this paper, we study the existence, uniqueness and stability of periodic solution for a wide class of memristor-based neural networks with time-varying delays. By employing the topological degree theory in set-valued analysis, differential inclusions theory and a new Lyapunov function method, we prove that the neural network has a unique periodic solution, which is globally exponentially stable. Moreover, we prove the existence, uniqueness and global exponential stability of equilibrium point for time-varying delayed memristor-based neural networks with constant coefficients. The obtained results improve and extend previous works on memristor-based or usual neural network dynamical systems with continuous or discontinuous right-hand side. Finally, two numerical examples are provided to show the applicability and effectiveness of our main results.