Improved delay-dependent stability conditions for recurrent neural networks with multiple time-varying delays

This paper investigates the global asymptotic stability problem for recurrent neural networks with multiple time-varying delays. Using the free-weighting matrix technique, and incorporating the interconnected information between the upper bounds of multiple time-varying delays, two less conservative delay-dependent asymptotic stability conditions are proposed, which are expressed by linear matrix inequalities, and can be conveniently solved by the existing softwares. Numerical examples show the reduce conservatism of the obtained conditions.     

Global exponential stability of stochastic memristor-based complex-valued neural networks with time delays

In recent years, the dynamic behaviors of complex-valued neural networks have been extensively investigated in a variety of areas. This paper focuses on the stability of stochastic memristor-based complex-valued neural networks with time delays. By using the Lyapunov stability theory, Halanay inequality and Itô formula, new sufficient conditions are obtained for ensuring the global exponential stability of the considered system. Moreover, the obtained results not only generalize the previously published corresponding results as special cases for our results, but also can be checked with the parameters of system itself. Finally, simulation results in three numerical examples are discussed to illustrate the theoretical results.     

Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays

In this paper we consider a class of impulsive Caputo fractional-order cellular neural networks with time-varying delays. Applying the fractional Lyapunov method and Mittag-Leffler functions, we give sufficient conditions for global Mittag-Leffler stability which implies global asymptotic stability of the network equilibrium. Our results provide a design method of impulsive control law which globally asymptotically stabilizes the impulse free fractional-order neural network time-delay model. The synchronization of fractional chaotic networks via non-impulsive linear controller is also considered. Illustrative examples are given to demonstrate the effectiveness of the obtained results.     

GLOBAL EXPONENTIAL STABILITY OF HOPFIELD NEURAL NETWORKS WITH VARIABLE DELAYS AND IMPULSIVE EFFECTS

A class of Hopfield neural network with time-varying delays and impulsive effects is concerned. By applying the piecewise continuous vector Lyapunov function some sufficient conditions were obtained to ensure the global exponential stability of impulsive delay neural networks. An example and its simulation are given to illustrate the effectiveness of the results.     

Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure

In this paper, based on switched systems and recurrent neural networks (RNNs) with time-varying delay, the model of switched RNNs is formulated. Global asymptotical stability (GAS) and global robust stability (GRS) for such switched neural networks are studied by employing nonlinear measure and linear matrix inequality (LMI) techniques. Some new sufficient conditions are obtained to ensure GAS or GRS of the unique equilibrium of the proposed switched system. Furthermore, the proposed LMI results are computationally efficient as it can be solved numerically with standard commercial software. Finally, three examples are provided to illustrate the usefulness of the results.     

State estimation for Markovian jumping recurrent neural networks with interval time-varying delays

The paper is concerned with the state estimation problem for a class of neural networks with Markovian jumping parameters. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error are globally stable in the mean square. A new type of Markovian jumping matrix P _i is introduced in this paper. The discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Delay-independent exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

Different from the approaches used in the earlier papers, in this paper, the Halanay inequality technique, in combination with the Lyapunov method, is exploited to establish a delay-independent sufficient condition for the exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms. Moreover, for the deterministic delayed Cohen–Grossberg neural networks, with or without reaction–diffusion terms, sufficient criteria for their global exponential stability are also obtained. The proposed results improve and extend those in the earlier literature and are easier to verify. An example is also given to illustrate the correctness of our results.     

Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions

In this paper, the global robust exponential stability of interval neural networks with delays and inverse Hölder neuron activation functions is considered. By using linear matrix inequality (LMI) techniques and Brouwer degree properties, the existence and uniqueness of the equilibrium point are proved. By applying Lyapunov functional approach, a sufficient condition which ensures that the network is globally robustly exponentially stable is established. A numerical example is provided to demonstrate the validity of the theoretical results.     

Global asymptotic stability of cellular neural networks with proportional delays

Proportional delay, which is different from distributed delay, is a kind of unbounded delay. The proportional delay system as an important mathematical model often rises in some fields such as physics, biology systems, and control theory. In this paper, the uniqueness and the global asymptotic stability of equilibrium point of cellular neural networks with proportional delays are analyzed. By using matrix theory and constructing suitable Lyapunov functional, delay-dependent and delay-independent sufficient conditions are obtained for the global asymptotic stability of cellular neural networks with proportional delays. These results extend previous works on these issues for the delayed cellular neural networks. Two numerical examples and their simulation are given to illustrate the effectiveness of obtained results.     

GLOBAL STABILITY ANALYSIS IN CELLULAR NEURAL NETWORKS WITH UNBOUNDED TIME DELAYS

Without assuming the boundedness and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of cellular neural networks with unbounded time delays and variable delays were studied. Using the idea of vector Liapunov method, the intero-differential inequalities with unbounded delay and variable delays were constructed. By the stability analysis of the intero-differential inequalities, the sufficient conditions for global asymptotic stability of cellular neural networks were obtained.     

Global stability and stabilization for inertial memristive neural networks with unbounded distributed delays

Nonlinear Dynamics - This paper investigates the stability and stabilization of inertial memristive neural networks (IMNNs) with discrete and unbounded distributed delays. The considered IMNNs are...     

Passivity analysis of uncertain neural networks with mixed time-varying delays

This paper addresses the passivity problem for uncertain neural networks with both discrete and distributed time-varying delays. It is assumed that the parameter uncertainties are norm-bounded. By construction of an augmented Lyapunov–Krasovskii functional and utilization of zero equalities, improved passivity criteria for the networks are derived in terms of linear matrix inequalities (LMIs) via new approaches. Through three numerical examples, the effectiveness to enhance the feasible region of the proposed criteria is demonstrated.     

On improved passivity criteria of uncertain neural networks with time-varying delays

In this paper, the problem of passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii’s functional and some novel analysis techniques, improved delay-dependent criteria for checking the passivity of the neural networks are established. The proposed criteria are represented 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 superiority of our results.     

Function projective synchronization of impulsive neural networks with mixed time-varying delays

In this paper, the exponential function projective synchronization of impulsive neural networks with mixed time-varying delays is investigated. Based on the contradiction method and analysis technique, some novel criteria are obtained to guarantee the function projective synchronization of considered networks via combining open-loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization, and the stabilization of the addressed neural networks. Finally, two examples and their numerical simulations are given to show the effectiveness and feasibility of the proposed synchronization schemes.     

The stability in neural networks with interneuronal transmission delays

1.IntroductionInthispaper,westudythefollowingmodelofaneuralwithnunits:inwhichfi(t)correspondstothemembranepotentialofthei-thunitattimet;h(xj)denotestheconversionofthemembranepotentialofthe.l-thunitsintoitsfiringrate:coildellotesthestrengthofthej-thunit;accorrespondStothetransmissiondelayalongtheaxonofthe.j-thunit;theConstantpid,enotestheexternalbiasorclampedinputfi-omoutsidethenetworktothei-thunit:hirepresentstheratewithwhichtheI-thLlnltwillresetitspotentialtotherestingstateinisolationwhendis…     

Global stabilization of fractional-order memristor-based neural networks with incommensurate orders and multiple time-varying delays: a positive-system-based approach

Nonlinear Dynamics - This paper addresses global stabilization of fractional-order memristor-based neural networks (FMNNs) with incommensurate orders and multiple time-varying delays (MTDs), where...     

Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch

In this paper, the projective synchronization of neural networks with mixed time-varying delays and parameter mismatch is discussed. Due to parameter mismatch and projective factor, complete projective synchronization cannot be achieved. Therefore, a new weak projective synchronization scheme is proposed to ensure that coupled neural networks are in a state of synchronization with an error level. Several criteria are derived and the error level is estimated by applying a generalized Halanay inequality and matrix measure. Finally, a numerical example is given to verify the efficiencies of theoretical results.     

Global exponential estimates for uncertain Markovian jump neural networks with reaction-diffusion terms

In this paper, the robust global exponential estimating problem is investigated for Markovian jumping reaction-diffusion delayed neural networks with polytopic uncertainties under Dirichlet boundary conditions. The information on transition rates of the Markov process is assumed to be partially known. By introducing a new inequality, some diffusion-dependent exponential stability criteria are derived in terms of relaxed linear matrix inequalities. Those criteria depend on decay rate, which may be freely selected in a range according to practical situations, rather than required to satisfy a transcendental equation. Estimates of the decay rate and the decay coefficient are presented by solving these established linear matrix inequalities. Numerical examples are provided to demonstrate the advantage and effectiveness of the proposed method.     

Global asymptotic stability for Hopfield-type neural networks with diffusion effects

The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.