Exponential Stability Of Neural Networks Research Articles

Global Exponential Stability of Time Varying Delay Memristor Neural Networks with Impulses

This paper, we mainly study the global exponential stability of neural networks with impulses for time-varying delay Memristor models. By using the Lyapunov stability theory and the matrix measure method, the conditions for the global exponential stability of neural networks of time-varying delay Memristor with impulsive efects are proposed and proved. Then several examples were provided to demonstrate the efectiveness of the obtained results.

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

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

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

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

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

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

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

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

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

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

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

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

Improved exponential stability criteria for time-varying delayed neural networks

Improved exponential stability criteria for time-varying delayed neural networks

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

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

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

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

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

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

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

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