Exponential stability analysis for uncertain neural networks with interval time-varying delays

In this paper, the problem of exponential stability analysis for neural networks is investigated. It is assumed that the considered neural networks have norm-bounded parametric uncertainties and interval time-varying delays. By constructing a new Lyapunov functional, new delay-dependent exponential stability criteria with an exponential convergence rate are established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the effectiveness of proposed criteria.     

Exponential stability analysis for neutral switched systems with interval time-varying mixed delays and nonlinear perturbations

This paper is concerned with the problem of exponential stability for uncertain neutral switched systems with interval time-varying mixed delays and nonlinear perturbations. By using the average dwell time approach and the piecewise Lyapunov functional technique, some sufficient conditions are first proposed in terms of a set of linear matrix inequalities (LMIs), to guarantee the robustly exponential stability for the uncertain neutral switched systems, where the decay estimate is explicitly given to quantify the convergence rate. Three numerical examples are finally illustrated to show the effectiveness of the proposed method.     

Delay-range-dependent robust H filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters

This paper investigates the problem of robust H^∞ filtering for uncertain stochastic time-delay systems with Markovian jump parameters. Both the state dynamics and measurement of the system are corrupted by Wiener processes. The time delay varies in an interval and depends on the mode of operation. A Markovian jump linear filter is designed to guarantee robust exponential mean-square stability and a prescribed disturbance attenuation level of the resulting filter error system. A novel approach is employed in showing the robust exponential mean-square stability. The exponential decay rate can be directly estimated using matrices of the Lyapunov-Krasovskii functional and its derivative. A delay-range-dependent condition in the form of LMIs is derived for the solvability of this H^∞ filtering problem, and the desired filter can be constructed with solutions of the LMIs. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Further results on mean square exponential stability of uncertain stochastic delayed neural networks

In this paper, the mean square exponential stability problem is deal with for a class of uncertain stochastic neural networks with time-varying delays. By introducing a new Lyapunov–Krasovskii function, improved delay-dependent stability criteria are established in term of linear matrix inequalities (LMIs). Finally, two numerical examples are given to show that our results are less conservative and more efficiency than the existing stability criteria.     

Exponential stability of recurrent neural networks with time-varying discrete and distributed delays

This paper is concerned with the problems of determining the global exponential stability and estimating the exponential-convergence rate for a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. By constructing an appropriate Lyapunov–Krasovskii functional and employing linear matrix inequality (LMI) technique, new delay-dependent exponential-stability criteria are derived in term of LMIs and the exponential-convergence rate is estimated. Numerical examples are given to show the effectiveness and improvement of the obtained results.     

Cohen-Grossberg神经网络指数稳定性的新判则

避免构造Lyapunov函数的困难,运用广义Dahlquist数方法研究了Cohen- Grossberg神经网络模型的指数稳定性,不但得到了Cohen-Grossberg神经网络平衡点存在惟一性和指数稳定性的全新充分条件,而且给出了神经网络的指数衰减估计.与已有文献结果相比,所得的神经网络指数稳定的充分条件更为宽松,给出的解的指数衰减速度估计也更为精确.     

Exponential stability for stochastic BAM networks with discrete and distributed delays

In this paper, we investigate exponential stability for stochastic BAM networks with mixed delays. The mixed delays include discrete and distributed time-delays. The purpose of this paper is to establish some criteria to ensure the delayed stochastic BAM neural networks are exponential stable in the mean square. A sufficient condition is established by consructing suitable Lyapunov functionals. The condition is expressed in terms of the feasibility to a couple LMIs. Therefore, the exponential stability of the stochastic BAM networks with discrete and distributed delays can be easily checked by using the numerically efficient Matlab LMI toobox. A simple example is given to demonstrate the usefulness of the derived LMI-based stability conditions.     

Robust Stabilization of Linear Systems with Delayed State and Control

Robust stabilization of linear systems with delays on both the state and control input is studied in this paper. Using an improved Lyapunov-Krasovskii functional, we establish new criteria that ensure the robust stability of the closed-loop system with memoryless state feedback controls. The generalized conditions are derived in terms of linear matrix inequalities (LMIs), allowing us to compute simultaneously the two bounds that characterize the exponential stability rate of the solution and can be easily solved by numerical algorithms. This work was supported by the National Basic Program in Natural Sciences. The authors thank the anonymous referees for valuable comments to improve the paper.     

Delay-dependent exponential stability for a class of neural networks with time delays

This paper is concerned with the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type. In terms of a linear matrix inequality (LMI), a sufficient condition guaranteeing the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks is proposed. This condition is dependent on the size of the time delay, which is usually less conservative than delay-independent ones. The proposed LMI condition can be checked easily by recently developed algorithms solving LMIs. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

Improved results on robust exponential stability criteria for neutral-type delayed neural networks

In this paper, we investigate the problem of robust global exponential stability analysis for a class of neutral-type neural networks. The interval time-varying delays allow for both slow and fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. Improved global exponential stability condition is derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed nominal and robust stability criteria is delay-dependent and characterized by linear-matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.     

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters

This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequality (LMI) by constructing new Lyapunov-Krasovskii functionals via generalized eigenvalue problems (GEVPs). The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

On exponential stability of neutral delay differential system with nonlinear uncertainties

In this paper, the exponential stability for neutral delay differential system with nonlinear uncertainties is investigated. A novel exponential stability criterion for the system is derived using generalized eigenvalue problem (GEVP) approach. Based on this approach, the maximum allowable length and convergence rate is obtained. These stability conditions are formulated as linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. Numerical examples are given to illustrate the usefulness of our proposed method.     

Delay-range-dependent exponential stability criteria and decay estimation for switched Hopfield neural networks of neutral type

This paper is concerned with the problem of delay-range-dependent global exponential stability and decay estimation for a class of switched Hopfield neural networks (SHNNs) of neutral type. An average dwell time method is introduced into switched Hopfield neural networks. By constructing a new Lyapunov–Krasovskii functional and designing a switching law, some criteria are proposed for guaranteeing exponential stability for a given system, while the exponential decay estimation is explicitly developed for the states. A numerical example is provided to demonstrate the effectiveness of the main results.     

Neural networks with discrete and distributed time-varying delays: A general stability analysis

In this paper, the global asymptotic and exponential stability are investigated for a class of neural networks with both the discrete and distributed time-varying delays. By using appropriate Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique, several delay-dependent sufficient conditions are obtained to guarantee the global asymptotic and exponential stability of the addressed neural networks. These conditions are expressed in terms of LMIs, and are dependent on both the discrete and distributed time delays. Therefore, the stability of the neural networks can be checked readily by resorting to the Matlab LMI toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the differentiability of the discrete and distributed time-varying delays, which means that our results generalize and further improve those in the earlier publications. A simulation example is given to show the effectiveness and less conservatism of the obtained conditions.     

Exponential stability of impulsive nonlinear stochastic differential equations with mixed delays

This paper is concerned with the problem of exponential stability for a class of impulsive nonlinear stochastic differential equations with mixed time delays. By applying the Lyapunov–Krasovskii functional, Dynkin formula and Razumikhin technique with a stochastic version as well as the linear matrix inequalities (LMIs) technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. The obtained results generalize and improve some recent results. In particular, our results are expressed in terms of LMIs, and thus they are more easily verified and applied in practice. Finally, a numerical example and its simulation are given to illustrate the theoretical results.     

Global exponential stability of impulsive discrete-time neural networks with time-varying delays

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria.     

基于LMI方法的多时滞随机神经网络的指数稳定性

研究了一类具有多个时滞的随机神经网络的均方指数稳定性问题,应用Lyapunov-Krasovskii泛函稳定理论和线性矩阵不等式(LMI)方法,建立了该系统解的指数稳定判别准则,最后通过数值举例阐述了结果的有效性.     

Global robust exponential stability of delayed neural networks: An LMI approach

In this paper, the problems of determining the robust exponential stability and estimating the exponential convergence rate for neural networks with parametric uncertainties and time delay are studied. Based on Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique, some delay-dependent criteria are derived to guarantee global robust exponential stability. The exponential convergence rate can be easily estimated via these criteria.     

Asymptotic Stability of Traveling Wave Solutions for Perturbations with Algebraic Decay

For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation of the traveling wave profile decays at an algebraic rate, then the solution is shown to converge to a shifted wave profile at a corresponding temporal algebraic rate, and optimal intermediate results that combine temporal and spatial decay are obtained. The proofs are based on a general interpolation principle which says that algebraic decay results of this form always follow if exponential temporal decay holds for perturbation with exponential spatial decay and the wave profile is stable for general perturbations.     

A delay decomposition approach to stability analysis of neutral systems with time-varying delay

This paper presents novel stability criteria for neutral systems with time-varying delay. By developing a delayed decomposition approach, information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs). Then, based on the Lyapunov method, delay-dependent stability criteria are devised by taking the relationship between terms in the Leibniz-Newton formula into account. Criteria are derived in terms of LMIs, which can be easily solved by using various convex optimization algorithms. Three illustrative numerical examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.