Stability Of Discrete-time Neural Networks Research Articles

Delay-dependent Lurie–Postnikov type Lyapunov–Krasovskii functionals for stability analysis of discrete-time delayed neural networks

This paper addresses the influence of time-varying delay and nonlinear activation functions with sector restrictions on the stability of discrete-time neural networks. Compared to previous works that mainly focuses on the influence of delay information, this paper devotes to activation nonlinear functions information to help compensate the analysis technique based on Lyapunov–Krasovskii functional (LKF). A class of delay-dependent Lurie–Postnikov type integral terms involving sector constraints of nonlinear activation function is proposed to complement the LKF construction. The less conservative criteria for the stability analysis of discrete-time delayed networks is given by using improved LKF. Numerical examples show that conservatism can be reduced by the delay-dependent integral terms involving nonlinear activation functions.

On H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${H}_\\infty $$\\end{document} Finite-Time Boundedness and Finite-Time Stability for Discrete-Time Neural Networks with Leakage Time-Varying Delay

This paper investigates the problems of H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_\\infty $$\\end{document} finite-time boundedness (FTB) and finite-time stability (FTS) for discrete-time neural networks (NNs) with both leakage delay and discrete delay, as well as different generalized activation functions. To this end, we construct suitable Lyapunov–Krasovskii (L–K) functionals and apply the extended reciprocally convex approach to derive delay-dependent criteria for the addressed problems. The obtained conditions are expressed as linear matrix inequalities (LMIs), which can be efficiently solved by the LMI Toolbox in Matlab. The paper also admits of two numerical examples to point up the advantages and reliability of the proposed method.

Stability Analysis of Discrete-Time Neural Networks With a Time-Varying Delay: Extended Free-Weighting Matrices Zero Equation Approach.

This research investigates the stability of discrete-time neural networks (DNNs) with a time-varying delay by using the Lyapunov-Krasovskii functional (LKF) method. Recent researches acquired some less conservatism stability criteria for time-varying delayed systems via some augmented LKFs. However, the forward difference of such LKFs resulted in high-degree time-varying delay-dependent polynomials. This research aims to develop some augmented state-related vectors and the corresponding extended free-weighting matrices zero equations to avoid the appearance of such high-degree polynomials and help to provide more freedom for the estimation results. Besides, an augmented delay-product-type LKF is also established for ameliorating the stability conditions of the time-varying delayed DNNs. Then, based on the above methods and Jensen's summation inequality, the auxiliary-function-based summation inequality, and the reciprocally convex matrix inequality, some less conservatism stability criteria for time-varying delayed DNNs are formulated. The validity of the proposed time-varying delay-dependent stability criteria is illustrated by two numerical examples.

Exponential Stability of Discrete-Time Neural Networks With Large Delay.

We study the exponential stability of discrete-time neural networks (NNs) with a time-varying delay which contains a few intermittent large delays (LDs). By modeling the considered discrete-time NN as a discrete-time switched NN which contains two subsystems and one of them may be unstable over the LD periods (LDPs), switching techniques are employed to analyze the problem. Delay-dependent exponential stability conditions to check the frequency and the length of the LDs allowed for guaranteeing the exponential stability are proposed by applying a novel Lyapunov-Krasovskii functional (LKF) with LDP-based terms, Wirtinger-based summation inequality, and reciprocally convex combination technique. Based on these conditions, associated evaluation algorithms are developed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

Stability analysis of discrete-time neural networks with an interval-like time-varying delay

This paper studies the stability of discrete-time neural networks with an interval-like time-varying delay via the Lyapunov–Krasovskii (L–K) functional method. Firstly, a general free-matrix-based (GFMB) summation inequality is proposed, which includes the auxiliary-function-based and conventional free-matrix-based ones. Secondly, a novel L–K functional is deliberately constructed to make full advantage of the newly-developed GFMB summation inequality. Finally, a new stability condition is derived and two widely-used numerical examples are presented to show the effectiveness of the proposed approach.

Comparison principle for difference equations with variable-time impulses

In this paper, a class of difference equations with variable-time impulses is considered. By applying comparison principle, we shall show that difference equations with variable-time impulse can be reduced to the corresponding difference equations with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the difference equations with variable-time impulses. Furthermore, we use a series of sufficient criteria to illustrate the same stability properties between variable-time impulsive difference equations and the fixed-time ones. We then establish several sufficient conditions guaranteeing the global exponential stability of variable-time impulsive difference equations by comparison principle. As an application, global exponential stability of discrete-time neural networks with variable-time impulses is discussed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.

Improved criteria of delay-dependent stability for discrete-time neural networks with leakage delay

This paper is concerned with the stability analysis of discrete-time neural networks with leakage and time-varying delays. By a novel summation inequality, the technique of reciprocally convex combination and triple Lyapunov–Krasovskii terms, the various cases of time-delay are discussed in detail and improved criteria are established to ensure the delay-dependent stability of discrete-time neural networks. Finally, three examples are given to verify the effectiveness of the proposed methods.

A Halanay-type inequality approach to the stability analysis of discrete-time neural networks with delays

In this paper, we consider the stability of discrete-time neural networks with time-varying delays. A new discrete-time Halanay-type inequality is presented, based on which, we derive sufficient conditions for the globally asymptotic and exponential stability of discrete-time delayed neural networks. Two kinds of neural networks, without and with impulsive effects are investigated. Numerical examples and simulations are given to illustrate the effectiveness of the obtained results.

Dynamics of Uncertain Discrete-Time Neural Network with Delay and Impulses

The stability of discrete-time impulsive delay neural networks with and without uncertainty is investigated. First, by using Razumikhin-type theorem, a new less conservative condition for the exponential stability of discrete-time neural network with delay and impulse is proposed. Moreover, some new sufficient conditions are derived to guarantee the stability of uncertain discrete-time neural network with delay and impulse by using Lyapunov function and linear matrix inequality (LMI). Finally, several examples with numerical simulation are presented to demonstrate the effectiveness of the obtained results.

State Estimation for Discrete-Time Stochastic Neural Networks with Mixed Delays

This paper investigates the analysis problem for stability of discrete-time neural networks (NNs) with discrete- and distribute-time delay. Stability theory and a linear matrix inequality (LMI) approach are developed to establish sufficient conditions for the NNs to be globally asymptotically stable and to design a state estimator for the discrete-time neural networks. Both the discrete delay and distribute delays employ decomposing the delay interval approach, and the Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals, such that a new stability criterion is proposed in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness of the proposed method and the applicability of the proposed method.

Periodicity and exponential stability of discrete-time neural networks with variable coefficients and delays

Discrete analogues of continuous-time neural models are of great importance in numerical simulations and practical implementations. In the current paper, a discrete model of continuous-time neural networks with variable coefficients and multiple delays is investigated. By Lyapunov functional, continuation theorem of topological degree, inequality technique and matrix analysis, sufficient conditions guaranteeing the existence and globally exponential convergence of periodic solutions are obtained, without assuming the boundedness and differentiability of activation functions. To show the effectiveness of our method, an illustrative example is presented along with numerical simulations.MSC:34D23, 34K20, 39A12, 92B20.

New criteria on delay-dependent stability for discrete-time neural networks with time-varying delays

In this paper, the problem of delay-dependent stability for discrete-time neural networks with time-varying delays is investigated. By constructing a newly augmented Lyapunov–Krasovskii functional, a sufficient condition for guaranteeing the asymptotic stability of the concerned network is derived in the framework of linear matrix inequalities. Also, a further improved stability condition is developed by proposing a new activation condition which has not been considered in the literature. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

Global Exponential Stability of Discrete-Time Neural Networks with Time-Varying Delays

This paper presents some global stability criteria of discrete-time neural networks with time-varying delays. Based on a discrete-type inequality, a new global stability condition for nonlinear difference equation is derived. We consider nonlinear discrete systems with time-varying delays and independence of delay time. Numerical examples are given to illustrate the effectiveness of our theoretical results.

Exponential stability of discrete-time neural networks with delay and impulses

In this paper, we investigate the exponential stability of discrete-time neural networks with impulses and time-varying delay. The discrete-time neural networks are derived by discretizing the corresponding continuous-time counterparts with different discretization methods. The impulses are classified into three classes: input disturbances, stabilizing and “neutral” type – the impulses are neither helpful for stabilizing nor destabilizing the neural networks, and then by using the excellent ideology introduced recently by Chen and Zheng [W.H. Chen, W.X. Zheng, Global exponential stability of impulsive neural networks with variable delay: an LMI approach, IEEE Trans. Circuits Syst. I 56 (6) (2009) 1248–1259], the connections between the impulses and the utilized Lyapunov function are fully explored with respect to each type of impulse. Novel techniques that used to realize the ideology in discrete-time situation are proposed and it is shown that they are essentially different from the continuous-time case. Several criteria for global exponential stability of the discrete-time neural networks are established in terms of matrix inequalities and based on these theoretical results numerical simulations are given to compare the capability of different discretization methods.

Improved Criteria on Delay-Dependent Stability for Discrete-Time Neural Networks with Interval Time-Varying Delays

The purpose of this paper is to investigate the delay-dependent stability analysis for discrete-time neural networks with interval time-varying delays. Based on Lyapunov method, improved delay-dependent criteria for the stability of the networks are derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii functional and utilizing reciprocally convex approach. Also, a new activation condition which has not been considered in the literature is proposed and utilized for derivation of stability criteria. Two numerical examples are given to illustrate the effectiveness of the proposed method.

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.

Asymptotic stability for neural networks with mixed time-delays: The discrete-time case

This paper is concerned with the stability analysis problem for a new class of discrete-time recurrent neural networks with mixed time-delays. The mixed time-delays that consist of both the discrete and distributed time-delays are addressed, for the first time, when analyzing the asymptotic stability for discrete-time neural networks. The activation functions are not required to be differentiable or strictly monotonic. The existence of the equilibrium point is first proved under mild conditions. By constructing a new Lyapnuov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the discrete-time neural networks to be globally asymptotically stable. As an extension, we further consider the stability analysis problem for the same class of neural networks but with state-dependent stochastic disturbances. All the conditions obtained are expressed in terms of LMIs whose feasibility can be easily checked by using the numerically efficient Matlab LMI Toolbox. A simulation example is presented to show the usefulness of the derived LMI-based stability condition.

Global exponential stability for discrete-time neural networks with variable delays

This Letter provides new exponential stability criteria for discrete-time neural networks with variable delays. The main technique is to reduce exponential convergence estimation of the neural network solution to that of one component of the corresponding solution by constructing Lyapunov function based on M-matrix. By introducing the tuning parameter diagonal matrix, the delay-independent and delay-dependent exponential stability conditions have been unified in the same mathematical formula. The effectiveness of the new results are illustrated by three examples.

Global exponential stability of discrete-time neural networks for constrained quadratic optimization

A class of discrete-time recurrent neural networks for solving quadratic optimization problems over bound constraints is studied. The regularity and completeness of the network are discussed. The network is proven to be globally exponentially stable (GES) under some mild conditions. The analysis of GES extends the existing stability results for discrete-time recurrent networks. A simulation example is included to validate the theoretical results obtained in this letter.