Impulsive Neural Networks Research Articles

Distributed-delay-dependent exponential stability of impulsive neural networks with inertial term

Abstract Global exponential stability problem of impulsive inertial neural networks with time-varying discrete-delay and distributed-delay is considered in the present paper. Lyapunov–Krasovskii functional and differential inequality for delay differential equations are employed to investigate the stability of the inertial neural networks. The distributed-delay-dependent stability criteria are obtained in terms of linear matrix inequalities and algebraic inequalities. The novel results complement and extend the works on inertial neural network with/without impulsive effects. Finally, typical numerical examples are given to illustrate the validity of the theoretical results.

New Delay-Dependent Stability Criteria for Impulsive Neural Networks with Additive Time-Varying Delay Components and Leakage Term

This work is concerned with the delay-dependent stability problem for uncertain impulsive neural networks (NNs) with additive time-varying delay components and leakage term. We construct a newly augmented Lyapunov–Krasovskii (L–K) functional which contains triple and four integral terms and then utilizing free-matrix-based integral inequality to bound the derivative of the Lyapunov–Krasovskii functional. Some sufficient conditions are derived to assure the delay-dependent stability of the impulsive NNs by the linear matrix inequality, which is less conservative than some existing results and can be readily verified by the convex optimization algorithms. In addition, some information of activation function ignored in previous works has been taken into account in the resulting condition. In the end, three numerical examples are provided to illustrate the effectiveness of the proposed criteria.

New stability results for impulsive neural networks with time delays

This paper investigates the stability of impulsive neural networks with time delays. Based on a new tool called as uniformly exponentially convergent functions, an improved Razumikhin method leads to new, more permissive stability results. By comparison with the existing results, the rigorous restrictions on impulses, which are presented in the previous Razumikhin stability theorems, are removed. Moreover, the obtained results do not restrict that the time derivative of Lyapunov function is negative definite or positive definite under the Razumikhin condition. The effectiveness of the proposed results is demonstrated by three simple numerical examples.

Global exponential stability of Markovian jumping stochastic impulsive uncertain BAM neural networks with leakage, mixed time delays, and \u03b1-inverse H\xf6lder activation functions

This paper concerns the problem of enhanced results on robust finite time passivity for uncertain discrete time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov–Krasovskii functional candidate, reciprocally convex combination method, and linear matrix inequality technique, we derive several sufficient conditions for varying the passivity of discrete time BAM neural networks. Further, some sufficient conditions for finite time boundedness and passivity for uncertainties are proposed by employing zero inequalities. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.

Stability of quaternion-valued impulsive delay difference systems and its application to neural networks

Abstract In this paper, we make first attempt to investigate exponential stability for quaternion-valued impulsive delay difference systems. By employing Lyapunov methods and quaternion-modulus inequality technique, sufficient conditions for the exponential stability are presented. In addition, as a subsequent result, the obtained theory is successfully applied to study a class of discrete-time quaternion-valued impulsive neural networks with delay. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.

Global exponential stability of fractional‐order impulsive neural network with time‐varying and distributed delay

In this article, we present several results on global exponential stability of a fractional‐order cellular neural network with impulses and with time‐varying and distributed delay. By using the Lyapunov‐like function methods in conjunction with the Razumikhin techniques, we derive sufficient condition for the exponential stability with an exponential convergence rate. The obtained outcomes of our present investigation significantly extend and generalize the corresponding results existing in the current literature. Finally, we give 2 illustrative examples to demonstrate the theoretical findings.

Stability of Stochastic Differential Switching Systems with Time-Delay and Impulsive Effects

This paper studies the stability of hybrid impulsive and switching stochastic neural networks. First, a new type of switching signal is constructed. The stochastic differential switching systems are steerable under the work of the switching signals. Then, using switching Lyapunov function approach, Itô formula, and generalized Halanay’s inequality, some global asymptotical and global exponential stability criteria are derived. These criteria improve the existing results on hybrid systems without noises. An example is given to demonstrate the effectiveness of the results.

Uncertain impulsive differential systems of fractional order: almost periodic solutions

ABSTRACTIn this paper, we investigate the existence and stability of almost periodic solutions of impulsive fractional-order differential systems with uncertain parameters. The impulses are realised at fixed moments of time. For the first time, we determine the impact of the uncertainties on the qualitative behaviour of such systems. The main criteria for the existence of almost periodic solutions are proved by employing the fractional Lyapunov method. The global perfect robust uniform-asymptotic stability of such solutions is also considered. We apply our results to uncertain impulsive neural network systems of fractional order.

State feedback synchronization control of impulsive neural networks with mixed delays and linear fractional uncertainties

This study examines the synchronization problem of impulsive neural networks with mixed time-varying delays and linear fractional uncertainties. The mixed time-varying delays include distributed leakage, discrete and distributed time-varying delays. Moreover, the restrictions on derivatives of time-varying delays with upper bounds to smaller than one is relaxed by introducing free weight matrices. Based on suitable Lyapunov–Krasovskii functionals and integral inequalities, linear matrix inequality approach is used to derive the sufficient conditions that guarantee the synchronization criteria of impulsive neural networks via delay dependent state feedback control. Finally, three numerical examples are given to show the effectiveness of the theoretical results.

Fixed-time stability and stabilization of impulsive dynamical systems

This paper mainly tends to consider the fixed-time stability behavior for impulsive dynamical systems. An efficient theorem is established to construct an impulsive comparison system. By means of inequality analysis method, certain average impulsive interval and Lyapunov function, some sufficient conditions are given to ensure the fixed-time stability of impulsive dynamical systems. Moreover, as an important application, the fixed-time stabilization of a class of coupled impulsive neural networks is proposed. By designing a discontinuous control law, several new criteria are obtained to guarantee the fixed-time stabilization of the coupled impulsive neural networks. Finally, two numerical simulations are provided to illustrate the validity of the theoretical analysis.

Event-triggered state estimation for Markovian jumping impulsive neural networks with interval time-varying delays

ABSTRACTThis paper investigates the event-triggered state estimation problem of Markovian jumping impulsive neural networks with interval time-varying delays. The purpose is to design a state estimator to estimate system states through available output measurements. In the neural networks, there are a set of modes, which are determined by Markov chain. A Markovian jumping time-delay impulsive neural networks model is employed to describe the event-triggered scheme and the network- related behaviour, such as transmission delay, data package dropout and disorder. The proposed event-triggered scheme is used to determine whether the sampled state information should be transmitted. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. First, we design a state observer to estimate the neuron states. Second, based on a novel Lyapunov-Krasovskii functional (LKF) with triple-integral terms and using an improved inequality, several sufficient conditions are derived. The derived conditions are formulated in terms of a set of linear matrix inequalities , under which the estimation error system is globally asymptotically stable in the mean square sense. Finally, numerical examples are given to show the effectiveness and superiority of the results.

Further improved results on stability and dissipativity analysis of static impulsive neural networks with interval time-varying delays

This paper deals with the problem of stability and dissipativity analysis for a class of static neural networks (SNNs) with interval time-varying delays. The system under study involves impulsive effects and time delays, which are often encountered in practice and are the sources of instability. Our attention is focused on the an analysis of whether the system is asymptotically stable and strictly (Q,S,R)−γ- dissipative. Based on the Wirtinger-based single and double integral inequality technique combined with the free-weighting-matrix approach which is expressed in terms of linear matrix inequalities (LMIs), we propose an improved delay-dependent stability and dissipativity criterion to guarantee the system to be admissible. Based on this criterion, a new sufficient delay and γ-dependent condition is given to guarantee that the SNNs with interval time-varying delays are strictly (Q,S,R)−γ- dissipative. Finally, the results developed in this paper can tolerate larger allowable delay bounds than the existing ones in the recent literature, which is demonstrated by several interesting examples.

Stability analysis for neutral-type impulsive neural networks with delays

Stability analysis for neutral-type impulsive neural networks with delays

Stability of Variable-Time Impulsive Systems with Delays via Generalized Razumikhin Technique and Application to Impulsive Neural Networks

This paper investigates the stability of variable-time impulsive systems with time delays. A novel stability result is obtained via the generalized Razumikhin technique. By viewing fixed-time impulsive systems as degenerative variable-time impulsive systems, a new stability result for fixed-time impulsive systems is also proposed. In order to demonstrate the effectiveness of the generalized Razumikhin technique, we give some comparison results with the existing stability criteria which are derived from the classical Razumikhin technique. Stability of impulsive neural networks and synchronization of complex networks are employed to indicate the effectiveness and the practicality of the theoretical results.

Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition

This paper is concerned with the stability analysis issue of fractional-order impulsive neural networks. Under the one-side Lipschitz condition or the linear growth condition of activation function, the existence of solution is analyzed respectively. In addition, the existence, uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive neural networks with one-side Lipschitz condition are investigated by the means of contraction mapping principle and Lyapunov direct method. Finally, an example with numerical simulation is given to illustrate the validity and feasibility of the proposed results.

Periodicity and stability for variable-time impulsive neural networks

The paper considers a general neural networks model with variable-time impulses. It is shown that each solution of the system intersects with every discontinuous surface exactly once via several new well-proposed assumptions. Moreover, based on the comparison principle, this paper shows that neural networks with variable-time impulse can be reduced to the corresponding neural network with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the variable-time impulsive neural networks. Furthermore, a series of sufficient criteria are derived to ensure the existence and global exponential stability of periodic solution of variable-time impulsive neural networks, and to illustrate the same stability properties between variable-time impulsive neural networks and the fixed-time ones. The new criteria are established by applying Schaefer’s fixed point theorem combined with the use of inequality technique. Finally, a numerical example is presented to show the effectiveness of the proposed results.

Exponential Stability and Periodic Solutions of Impulsive Neural Network Models with Piecewise Constant Argument

In this paper we introduce an impulsive cellular neural network models with piecewise alternately advanced and retarded argument. The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique periodic solution. The approaches are based on employing Banach’s fixed point theorem and a new integral inequality of Gronwall type with impulses and deviating arguments. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses and piecewise constant argument deviations, which provides flexibility for the design and analysis of cellular neural network models. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results.

Stability Analysis of Impulsive Neural Networks with Piecewise Constant Arguments

The global exponential stability problem is considered for a class of impulsive neural networks with piecewise constant arguments in this paper. By employing the Banach fixed point theorem and the Razumikhin-type technique, stability criterion is obtained for the existence, uniqueness and global exponential stability of the periodic solution. Typical numerical examples are given to illustrate the improvement in less conservatism of the results.

Exponential Synchronization of the Hopfield Neural Networks with New Chaotic Strange Attractor

This paper studies the problems of exponential synchronization for the Hopfield neural networks with impulsive effects and Gui chaotic strange attractor. By employing the Lyapunov functional method of impulsive functional differential equations, some criteria for synchronization between two impulsive neural networks are derived. An illustrative example is provided to show the effectiveness and feasibility of the proposed method and results.

Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.