Exponential Stability Of Neural Networks Research Articles

Exponential stability of neural networks with a time-varying delay via a cubic function negative-determination lemma

The problem of global exponential stability of neural networks with a time-varying delay is studied in this article. Firstly, to fully utilize the cross-term relationships among state variables, an improved augmented delay-product-type Lyapunov-Krasovskii functional, including an extra double integral state, is established for the stability analysis. Accordingly, this augmented LKF derivative is a higher-order function of the time-varying delay. Then, three state vectors are considered to reduce the order of the function to cubic. So, to obtain the feasible negative-definiteness condition of this LKF derivative of non-convexity, a negative-determination lemma for cubic functions is employed to handle this problem. As a result, a novel stability criterion is obtained. Two well-known numerical examples illustrate the effectiveness of the criterion.

Free-weighting-matrix inequality for exponential stability for neural networks with time-varying delay

Exponential stability for neural networks with time-varying delay is considered in this paper. By extending the generalized free-weighting-matrix integral inequality, a novel integral inequality is derived by using weighted orthogonal functions. Then the new inequality is applied to investigate the exponential stability of time delay neural networks via an improved Lyapunov–Krasovskii functional. Numerical examples are given to verify the advantages of the proposed criterion.

Exponential Stabilization of Memristor-based Recurrent Neural Networks with Disturbance and Mixed Time Delays via Periodically Intermittent Control

A periodically intermittent control is considered for the memristor-based recurrent neural networks with disturbance and mixed time delays. The purpose of this study is to design the controller with less constraints, which is convenient for successful applications of memristor-based recurrent neural networks in complex environment. First, the estimate of the disturbance and mixed time delay are given by the assumptions. Then, by the method of Lyapunov-Krasovski functional, two new criteria ensuring globally exponential stabilization of the neural network are obtained under the controller, respectively. The proposed theoretical results indicate that the control width and control period are not constrained except that the control width has an upper bound. Furthermore, the design algorithm of controller is described. Finally, two examples are performed through four neural networks to illustrate the effectiveness of the proposed results.

Stability analysis of Hopfield neural networks with unbounded delay driven by G-Brownian motion

This paper is concerned with Hopfield neural networks with unbounded time-varying delay driven by G-Brownian motion. The existence and uniqueness of solutions, as well as the continuity of solutions in the sense of G-mean square, are investigated for such neural networks. Moreover, sufficient conditions dependent on delay are derived to guarantee G-mean square asymptotic stability and G-mean square exponential stability of neural networks. At last, two examples are provided to illustrate the application of the obtained results.

Synchronization of decentralized event-triggered uncertain switched neural networks with two additive time-varying delays

This paper addresses the problem of synchronization for decentralized event-triggered uncertain switched neural networks with two additive time-varying delays. A decentralized eventtriggered scheme is employed to determine the time instants of communication from the sensors to the central controller based on narrow possible information only. In addition, a class of switched neural networks is analyzed based on the Lyapunov–Krasovskii functional method and a combined linear matrix inequality (LMI) technique and average dwell time approach. Some sufficient conditions are derived to guarantee the exponential stability of neural networks under consideration in the presence of admissible parametric uncertainties. Numerical examples are provided to illustrate the effectiveness of the obtained results.

Almost sure exponential stabilization of neural networks by aperiodically intermittent control based on delay observations

This paper is concerned with almost sure exponential stabilization of neural networks by intermittent control based on delay observations. By the stochastic comparison principle and Itô’s formula, a sufficient criterion is derived, under which unstable neural networks can be stabilized by stochastic intermittent control based on delay observations. The range of intermittent rate is given, and the upper bound of time delay can be solved from a transcend equation. Finally, two examples are provided to demonstrate the feasibility and validity of our proposed methods.

Exponential Stability of Neural Networks with Markovian Switching Parameters and General Noise

This paper investigates the problem of exponential stability of Neural Networks (NNs) with Markovian parameters and general noise. The model in this paper with general noise is more suitable for many real nervous systems than NNs with white noise. Criteria for the exponential stability of the NNs with Markovian switching parameters and general noise in both the mean square and p-th moment are derived by utilizing the random analysis method and Lyapunov functional method techniques. The exponential stability of NNs without Markovian switching is given as a special case. Finally, simulation result in two examples are discussed to illustrate the theoretical results.

On Exponential Stability of Neural Networks with Proportional Delays and Periodic Distribution Impulsive Effects

This paper is concerned with the problem of generalized exponential stability of impulsive neural networks with a proportional delay. More specifically, the considered network models are subject to both time-varying impulses, whose strengths are in a type of periodic distributions, and a special kind of unbounded time-varying delays called proportional delays. Based on the comparison principle, a unified delay-independent stability criterion is first derived. As an application of the derived stability conditions, the problem of designing a local state feedback control law with bounded controller gains is addressed. Finally, three examples with numerical simulations are given to demonstrate the effectiveness and advantages of the results.

Delay-dependent global exponential stability for neural networks with time-varying delay

This paper deals with the global exponential stability problem of neural networks with time-varying delay. A novel Lyapounov–Krasovskii functional (LKF), which contains a common double integral term, an augmented double integral term and two delay-product-type terms, is constructed to analyze the exponential stability. An auxiliary function-based integral inequality (AFBII) and two special forms of it are applied to estimate the upper bounds of single integral terms produced in the time derivation of the LKF candidate. By using the novel LKF and AFBII, some new cross terms of matrix variables are included in linear matrix inequalities (LMIs). As a result, a less conservative delay-dependent global exponential stability criterion is proposed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed criterion.

Exponential stabilization of neural networks with time-varying delay by periodically intermittent control

This paper investigates the exponential stabilization of neural networks with time-varying delay by periodically intermittent control. By employing the free-matrix-based integral inequality and using some new analysis techniques, some novel exponential stabilization criteria are derived based on the Lyapunov–Krasovskii (L–K) functional method. The obtained criteria are in terms of linear matrix inequalities without transcendental equation, instead of nonlinear matrix inequalities, which reduces the computational burden. Compared to existing results in corresponding literatures, our results have a wider range of applications, and overcome no feasible solution if the information on the sizes of delays is ignored for the design of the intermittent controller. A numerical simulation is provided to show the effectiveness and the benefits of the theoretical results.

Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality

This paper is concerned with global exponential stability problem for a class of neural networks with time-varying delays. Using a new proposed inequality called free-matrix-based integral inequality, a less conservative criterion is proposed, which is expressed by linear matrix inequalities. Two numerical examples are given to show the effectiveness and superiority of the obtained criterion.

Delay-Dependent Criterion for Exponential Stability Analysis of Neural Networks with Time-Varying Delays

This note investigates the problem of exponential stability of neural networks with time-varying delays. To derive a less conservative stability condition, a novel augmented Lyapunov-Krasovskii functional (LKF) which includes triple and quadruple-integral terms is employed. In order to reduce the complexity of the stability test, the convex combination method is utilized to derive an improved delay-dependent stability criterion in the form of linear matrix inequalities (LMIs). The superiority of the proposed approach is demonstrated by two comparative examples.

Improved exponential stability criteria for time-varying delayed neural networks

This paper is concerned with the exponential stability for neural networks with mixed time-varying delays. By using a more general delay-partitioning approach, an augmented Lyapunov functional that contains some information about neuron activation function is constructed. In order to derive less conservative results, an adjustable parameter is introduced to divide the range of the activation function into two unequal subintervals. Moreover, the application of combination of integral inequalities further reduces the conservativeness of the obtained exponential stability conditions. Numerical examples illustrate the advantages of the proposed conditions when compared with other results from the literatures.

A weak condition for global stability of delayed neural networks

The classical analysis of asymptotical and exponential stability of neural networks needs assumptions on the existence of a positive Lyapunov function $V$ and on the strict negativity of the function $dV/dt$, which often come as a result of boundedness or uniformly almost periodicity of the activation functions. In this paper, we investigate the asymptotical stability problem of Hopfield neural networks with time delays under weaker conditions. By constructing a suitable Lyapunov function, sufficient conditions are derived to guarantee global asymptotical stability and exponential stability of the equilibrium of the system. These conditions do not require the strict negativity of $dV/dt $, nor do they require that the activation functions to be bounded or uniformly almost periodic.

Globally exponential stabilization of neural networks with mixed time delays via impulsive control

The impulsive stabilization problem of neural networks with discrete time-varying delays and unbounded continuously distributed delays is considered. By using impulse-time-dependent Lyapunov function-based techniques to capture the hybrid structure characteristics of the considered impulsive neural networks, two novel global exponential stability criteria are obtained in terms of linear matrix inequalities, which are capable of dealing with the case where both the continuous and discrete dynamics are unstable. When the original continuous-time delayed neural networks are not stable, sufficient conditions are developed for the design of exponentially stable linear impulsive state feedback controllers. Four numerical examples are given to illustrate the less conservatism and effectiveness of the proposed results.

Further results on exponential stability of neural networks with time-varying delay

This paper investigates the problem of the exponential stability for a class of neural networks with time-varying delay. A triple integral term and a term considering the delay information in a new way are introduced to the Lyapunov–Krasovskii functional (LKF). The obtained criterion show advantages over the existing ones since not only a novel LKF is constructed but also several techniques such as Wirtinger-based inequality and convex combination technique are used to estimate the upper bound of the derivative of the LKF. Finally, a numerical example is provided to verify the effectiveness and benefit of the proposed criterion.

A New Globally Exponential Stability Criterion for Neural Networks with Discrete and Distributed Delays

This paper concerns the problem of the globally exponential stability of neural networks with discrete and distributed delays. A novel criterion for the globally exponential stability of neural networks is derived by employing the Lyapunov stability theory, homomorphic mapping theory, and matrix theory. The proposed result improves the previously reported global stability results. Finally, two illustrative numerical examples are given to show the effectiveness of our results.

Exponential stability criterion for interval neural networks with discrete and distributed delays

This paper investigates the global exponential stability of neural networks with discrete and distributed delays. A new criterion for the exponential stability of neural networks with mixed delays is derived by using the Lyapunov stability theory, Homomorphic mapping theory and matrix theory. The obtained result is easier to be verified than those previously reported stability results. Finally, some illustrative numerical examples are given to show the effectiveness of the proposed result.

Almost surely exponential stability of neural networks with Lévy noise and Markovian switching

In this brief, the problem of almost surely exponential stability analysis is considered for neural networks with Lévy noise and Markovian switching. The switching parameters are generated from a continuous-time irreducible Markov chain taking value in a finite-state space. The purpose of the problem addressed is to derive a sufficient condition such that the dynamics of the neural network is almost surely exponentially stable. By generalized Itô׳s formula, strong law of large numbers for martingales and ergodicity of Markov chain, the stochastic analysis approach is developed to establish the desired condition which depends only on the stationary distribution of the Markov chain and some constants. Two numerical examples are given to verify the usefulness of the stability condition.

Dynamical Nonlinear Neural Networks with Perturbations Modeling and Global Robust Stability Analysis

paper is devoted to studying both the global and local stability of dynamical neural networks. In particular, it has focused on nonlinear neural networks with perturbation. Properties relating to asymptotic and exponential stability and instability have been detailed. This paper also looks at the robustness of neural networks to perturbations and examines if the related properties have been preserved. Circumstances for global and local exponential stability of nonlinear neural network dynamics have been studied. We mentioned that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point. From this, some well-known and new sufficient conditions for local exponential stability of neural networks have been obtained. The Lyapunov's procedure has been used to analyze the stability property of nonlinear dynamical systems and many outcomes have been combined and generalized. A kind of Lyapunov's stability of the stable points of Hopfield neural network (HNN) have been proven, which means that if the initial state of the network is close enough to a stable point, then the network state will remain in a small neighborhood of the stable point. These stability results indicate the convergence of the memory process of HNN. The theoretical results are illustrated through a few problem cases for a nonlinear dynamical system with perturbation behavior. Keywordserturbed nonlinear systems, Hopfield neural network,