Global Exponential Stability Analysis Research Articles

Global exponential stability criteria for neural networks with probabilistic delays

The problem of global exponential stability analysis for a class of neural networks (NNs) with probabilistic delays is discussed in this paper. The delay is assumed to follow a given probability density function. This function is discretised into arbitrary number of intervals. In this way, the NN with random time delays is transformed into one with deterministic delays and random parameters. New conditions for the exponential stability of such NNs are obtained by employing new Lyapunov-Krasovskii functionals and novel techniques for achieving delay dependence. It is established that these conditions reduce the conservatism by considering not only the range of the time delays, but also the probability distribution of their variation. Numerical examples are provided to show the advantages of the proposed techniques.

Analysis of global exponential stability and periodic solutions of FCNNs with constant delays and time-varying delays

In this paper, we investigate a class of fuzzy cellular neural networks with constant delays and time-varying delays. By constructing suitable Lyapunov functional and employing Young inequality, we find sufficient conditions for the existence, uniqueness, global exponential stability of equilibrium, and the existence of periodic solutions of fuzzy cellular neural networks with time-varying delays. The results of this paper are new and they extend previously known results.

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.

Improved exponential stability criteria for recurrent neural networks with time-varying discrete and distributed delays

In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks (RNNs) with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.

LMI-based exponential stability criterion for bidirectional associative memory neural networks

In this paper, we investigate the problem of global exponential stability analysis for a class of bidirectional associative memory (BAM) neural networks with interval time-delays. Improved exponential stability condition is derived by employing new Lyapunov–Krasovskii functional and the integral inequality. Several special cases of interest are derived. The developed stability criteria are delay dependent and characterized by linear matrix inequalities (LMIs). The developed results are shown to be less conservative than previous published ones in the literature. Finally, simulations of two numerical examples are provided to demonstrate the efficacy of our approach.

Improved Delay-Dependent Stability Condition of Discrete Recurrent Neural Networks With Time-Varying Delays

This brief investigates the problem of global exponential stability analysis for discrete recurrent neural networks with time-varying delays. In terms of linear matrix inequality (LMI) approach, a novel delay-dependent stability criterion is established for the considered recurrent neural networks via a new Lyapunov function. The obtained condition has less conservativeness and less number of variables than the existing ones. Numerical example is given to demonstrate the effectiveness of the proposed method.

An analysis of global exponential stability of neural networks with reaction-diffusion terms and distributed delays

A class of neural networks with reaction-diffusion terms and distributed delays is investigated. By constructing suitable Lyapunov functional, using M-matrix theory and some analysis techniques, some sufficient conditions have been given to ensure existence, uniqueness, and global exponential stability of equilibrium points of a class of neural networks with reaction-diffusion terms and distributed delays. Moreover, the exponential converging velocity index has been estimated, which depends on the delay kernel functions and system parameters. An example has been given to show the effectiveness of the obtained results.

Novel robust exponential stability criteria for neural networks

This paper investigates the problem of robust global exponential stability analysis for uncertain neural networks with interval time-varying delays. The time-delay pattern is quite general and including fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. The activation functions are monotone nondecreasing with known lower and upper bounds. Novel stability criteria are developed by employing new Lyapunov–Krasovskii functional and the integral inequality. The developed stability criteria are delay dependent and characterized by linear matrix inequalities (LMIs)-based conditions. The developed stability results are less conservative than previous published ones in the literature, which is illustrated by a representative numerical example.

Global exponential stability analysis of delayed Cohen–Grossberg neural networks with distributed delays [International Journal of Systems Science, Vol. 38 (2007) p. 601

In this article, we indicate that two proposed sufficient conditions in the paper by X.Y. Lou and B.T. Cui [International Journal of Systems Science, Vol. 38 (2007) p. 601] were incorrect in general, which cannot guarantee the existence and global exponential stability of the system's equilibrium. For correcting the mistakes, a correct version of global exponential stability is given and proved in this article.

Global Exponential Stability of Impulsive Neural Networks With Variable Delay: An LMI Approach

This paper focuses on the problem of global exponential stability analysis of impulsive neural networks with variable delay. Three types of impulses are considered: the impulses are input disturbances; the impulses are ldquoneutralrdquo type (that is, they are neither helpful for stability of neural networks nor destabilizing); and the impulses are stabilizing. For each type of impulses, by using Lyapunov function and Razumikhin-type techniques, the sufficient conditions for global exponential stability are developed in terms of linear matrix inequalities with respect to suitable classes of impulse time sequences. The new sufficient stability conditions do not impose any restriction on the size of time-delay. Numerical examples are given which show our results are less conservative than the existing sufficient stability conditions.

LMI-based Approach of Global Exponential Robust Stability for a Class of Uncertain Distributed Parameter Control Systems with Time-varying Delays

In this paper, the global exponential robust stability analysis problem is considered for a class of uncertain distributed parameter control systems with time-varying delays. The uncertain parameters are generated from modeling errors as well as parameter variations in the systems. The purpose of the problem addressed is to derive some easy-to-test conditions such that the dynamics of the uncertain system is globally exponentially robustly stable. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions and therefore global exponential robust stability for the uncertain distributed parameter control systems with time-varying delays can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.

Global exponential stability of cellular neural networks with time-varying discrete and distributed delays

This paper is concerned with the problem of global exponential stability analysis for a class of cellular neural networks with time-varying discrete and distributed delays (DDCNNs). A new delay-dependent sufficient condition is derived for the global exponential stability of the DDCNNs by using the integral inequality method and the newly proposed Lyapunov–Krasovskii functional. The obtained stability condition is less conservative than some of the existing results in the literature. Numerical examples are given to demonstrate the effectiveness and superiority of the proposed results.

Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays

In this paper, the global exponential stability is investigated for a class of stochastic interval neural networks with time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. Based on Lyapunov stable theory and stochastic analysis approaches, the delay-dependent criteria are derived to ensure the global, robust, exponential stability of the addressed system in the mean square. The criteria can be checked easily by the LMI control toolbox in Matlab. A numerical example is given to illustrate the effectiveness and improvement over some existing results.

Global exponential stability analysis of bidirectional associative memory neural networks with time-varying delays

In this paper, global exponential stability is studied for a class of high-order bidirectional associative memory (BAM) neural networks with time-varying delays. An approach combining the Lyapunov functional with the Linear Matrix Inequality (LMI) is taken to study the problems. Several sufficient conditions are presented for ensuring the system to be globally exponentially stable. Three typical examples are presented to show the application of the criteria obtained in this paper.

On delay-dependent robust exponential stability of stochastic neural networks with mixed time delays and Markovian switching

This paper deals with the global exponential stability analysis problem for a general class of uncertain stochastic neural networks with mixed time delays and Markovian switching. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed stochastic neural network is robustly exponentially stable in the mean square in the presence of parameters uncertainties, mixed time delays, and Markovian switching. By employing new Lyapunov–Krasovskii functionals and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria for the robust exponential stability, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. The criteria derived are dependent on both the discrete time delay and distributed time delay, and, are therefore, less conservative. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.

Global exponential stability analysis of delayed Cohen--Grossberg neural networks with distributed delays

In this article, the global exponential stability problem of Cohen--Grossberg neural networks with both discrete-time delays and distributed delays is investigated. The existence and global stability for the unique equilibrium of the Cohen--Grossberg neural networks with distributed delays are achieved by using some new Lyapunov functionals, M-matrix theory and some analytic techniques, and some less restrictive conditions are obtained. An example is also worked out to validate the advantages of our results.

Global exponential stability analysis of fuzzy BAM neural networks with time-varying delays

In this paper, the stability problem of Takagi-Sugeno fuzzy BAM neural networks with time-varying delays is considered. Firstly, this model is established as a modified Takagi-Sugeno fuzzy model in which the consequent parts are composed of a set of

Global exponential stability analysis for cellular neural networks with variable coefficients and delays

Some sufficient conditions for the global exponential stability of cellular neural networks with variable coefficients and time-varying delays are obtained by a method based on a delayed differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of cellular neural networks with variable coefficients and time-varying delays. Some previous results in the literature are shown to be special cases of our results.

Global exponential stability analysis of Cohen–Grossberg neural network with delays

This brief presents new sufficient conditions of globally exponential stability of Cohen–Grossberg neural networks with time delays. The results are also compared with previously reported results in the literature, implying that the results obtained in this paper provide one more set of criteria for determining the global exponential stability of Cohen–Grossberg neural networks with time delays.