Delay‐dependent robust stability analysis for interval neural networks with time‐varying delay

This article deals with the problem of robust stability for interval neural networks with time‐varying delay. By constructing an appropriate Lyapunov–Krasovskii functional, using the S‐procedure and taking the relationship among the time‐varying delay, its upper bound and their difference into account, some linear matrix inequality(LMI) ‐based delay‐dependent stability criteria are obtained without ignoring any terms in the derivative of the Lyapunov–Krasovskii functional. Finally, two numerical examples are given to demonstrate the effectiveness and benefits of the proposed method. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Global exponential stability of a class of impulsive cellular neural networks with supremums

In this paper, we study the problem of global exponential stability for impulsive cellular neural networks with time‐varying delays and supremums. Using Young's inequality and Lyapunov‐like functions, new stability criteria are proved. Because supremums and impulses are relevant in various contexts, including problems in the theory of automatic control, our results can be applied in the qualitative investigations of many practical problems of diverse interest. Copyright © 2013 John Wiley & Sons, Ltd.     

On global asymptotic stability for a class of delayed neural networks

This paper deals with the problem of stability analysis for a class of delayed neural networks described by nonlinear delay differential equations of the neutral type. A new and simple sufficient condition guaranteeing the existence, uniqueness and global asymptotic stability of an equilibrium point of such a kind of delayed neural networks is developed by the Lyapunov–Krasovskii method. The condition is expressed in terms of a linear matrix inequality, and thus can be checked easily by recently developed standard algorithms. When the stability condition is applied to the more commonly encountered delayed neural networks, it is shown that our result can be less conservative. Examples are provided to demonstrate the effectiveness of the proposed criteria. Copyright © 2011 John Wiley & Sons, Ltd.     

Global stability analysis of bidirectional associative memory neural networks with time delay

In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, we present new conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of bidirectional associative memory neural networks with fixed time delays or distributed time delays. The results are applicable to both symmetric and non‐symmetric interconnection matrices, and all continuous non‐monotonic neuron activation functions. Copyright © 2001 John Wiley & Sons, Ltd.     

Nonlinear Lipschitz measure and adaptive control for stability and synchronization in delayed inertial Cohen‐Grossberg–type neural networks

In this paper, without transforming the original inertial neural networks into the first‐order differential equation by some variable substitutions, time‐varying delays are introduced into inertial Cohen‐Grossberg–type networks and the existence, the uniqueness, and the asymptotic stability and synchronisation for the neural networks are investigated. Firstly, the existence of a unique equilibrium point is proved by using nonlinear Lipschitz measure method. Second, by finding a new Lyapunov‐Krasovskii functional, some sufficient conditions are derived to ensure the asymptotic stability, the asymptotic synchronization, and the asymptotic adaptive synchronization. The results of this paper are new and they complete previously known results. We illustrate the effectiveness of the approach through a few examples.     

Stability analysis of delayed fuzzy Cohen-Grossberg neural networks with discontinuous activations

In this article, we investigate the dynamical behavior of a class of delayed fuzzy Cohen-Grossberg neural networks (FCGNNs) with discontinuous activation functions subject to time delays and fuzzy terms. By using the inequality analysis technique and the M-matrix theory, sufficient and proper conditions are given in order to establish the existence, convergence, and global exponential stability of equilibrium point of the system. In particular, we discuss the impact of discontinuous neuron activations on the existence and exponential stability of equilibrium point for FCGNNs. Two numerical examples are provided to substantiate the theoretical results.     

Global exponential stability for uncertain bidirectional associative memory neural networks with multiple time‐varying delays via LMI approach

The global exponential stability for uncertain delayed bidirectional associative memory neural networks (DBAMNN) with multiple time‐varying delays is considered in this paper. Delay‐dependent criteria are proposed to guarantee the robust stability of DBAMNN via linear matrix inequality approach. Two classes of system uncertainties are investigated in this paper. Some numerical examples are given to illustrate the effectiveness of our results. From the numerical simulations, significant improvement over the recent results can be observed. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of leakage delay on global asymptotic stability of complex‐valued neural networks with interval time‐varying delays via new complex‐valued Jensen's inequality

This paper investigates the global asymptotic stability analysis for a class of complex‐valued neural networks with leakage delay and interval time‐varying delays. Different from previous literature, some sufficient information on a complex‐valued neuron activation function and interval time‐varying delays has been considered into the record. A suitable Lyapunov‐Krasovskii functional with some delay‐dependent terms is constructed. By applying modern integral inequalities, several sufficient conditions are obtained to guarantee the global asymptotic stability of the addressed system model. All the proposed criteria are formulated in the structure of a complex‐valued linear matrix inequalities technique, which can be checked effortlessly by applying the YALMIP toolbox in MATLAB linear matrix inequality. Finally, two numerical examples with simulation results have been provided to demonstrate the efficiency of the proposed method.     

Absolutely exponential stability in delayed cellular neural networks

In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, we present a necessary and sufficient condition ensuring the existence and uniqueness of the equilibrium point of cellular neural network with fixed time delays (DCNNs). Using M‐matrix theory, Liapunov functionals and functions are constructed and employed to establish sufficient conditions for absolutely exponential stability of DCNNs. The results are applicable to DCNNs with both symmetric and non‐symmetric interconnection matrices, and globally Lipschitz continuous activation functions. Copyright © 2002 John Wiley & Sons, Ltd.     

On complete stability of linear and quadratic programming neural networks

The paper addresses complete stability (CS) of the important class of neural networks to solve linear and quadratic programming problems introduced by Kennedy and Chua (IEEE Trans. Circuits Syst., 1988; 35 : 554). By CS it is meant that each trajectory converges to a stationary state, i.e. an equilibrium point of the neural network. It is shown that the neural networks in (IEEE Trans. Circuits Syst., 1988; 35 : 554) enjoy the property of CS even in the most general case where there are infinite non‐isolated equilibrium points. This result, which is proved by exploiting a new method to analyse CS (Int. J. Bifurcation Chaos 2001; 11 : 655), extends the stability analysis by Kennedy and Chua (IEEE Trans. Circuits Syst., 1988; 35 : 554) to situations of interest where the optimization problems have infinite solutions. Copyright © 2002 John Wiley & Sons, Ltd.     

Novel stability criteria for bidirectional associative memory neural networks with time delays

In this paper, the bidirectional associative memory (BAM) neural network with axonal signal transmission delay is considered. This model is also referred to as a delayed dynamic BAM model. By combining a number of different Lyapunov functionals with the Razumikhin technique, some sufficient conditions for the existence of a unique equilibrium and global asymptotic stability of the network are derived. These results are fairly general and can be easily verified. Besides, the approach for the analysis allows one to consider several different types of activation functions, including piecewise linear sigmoids with bounded activations as well as C¹‐smooth sigmoids. It is believed that these results are significant and convenient in the design and applications of BAM neural networks. Copyright © 2002 John Wiley & Sons, Ltd.     

Absolute stability of a class of neural networks with unbounded delay

In this paper, the existence and uniqueness of the equilibrium point and absolute stability of a class of neural networks with partially Lipschitz continue activation functions are investigated. The neural networks contain both variable and unbounded delays. Using the matrix property, the necessary and sufficient condition for the existence and uniqueness of the equilibrium point of the neural networks is obtained. By constructing proper vector Liapunov functions and non‐linear integro‐differential inequalities involving both variable delays and unbounded delay, the sufficient conditions for absolute stability (global asymptotic stability) are obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

Hyperbolic Hopfield neural networks with four‐state neurons

In recent years, applications of neural networks with Clifford algebra have become widespread. Clifford algebra is also referred to as geometric algebra and is useful in dealing with geometric objects. Hopfield neural networks with Clifford algebra, such as complex numbers and quaternions, have been proposed. However, it has been difficult to construct Hopfield neural networks by Clifford algebra with positive part of the signature, such as hyperbolic numbers. Hyperbolic numbers are useful algebra to deal with hyperbolic geometry. Kuroe proposed hyperbolic Hopfield neural networks and provided their continuous activation functions and stability conditions. However, the learning algorithm has not been provided. In this paper, we provide two quantized activation functions and the primitive learning algorithm satisfying the stability condition. We also perform computer simulations and compare the activation functions. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Event-triggered pinning synchronization and robust pinning synchronization of coupled neural networks with multiple weights

In this paper, we, respectively, solve the problems of event-triggered pinning synchronization and robust pinning synchronization of multiple weighted coupled neural networks (MWCNNs). By devising suitable event-triggered controller, some pinning synchronization and robust pinning synchronization criteria for MWCNNs with the appropriate event-triggered condition are deduced, respectively, on the basis of some inequalities and the theory of Lynapunov functional. Furthermore, we research the event-triggered pinning synchronization and event-triggered robust pinning synchronization of multiple weighted coupled delayed neural networks and establish some correlative synchronization criteria, respectively, on the basis of appropriate event-triggered condition and pinning controller. At last, the numerical simulation results in two examples verify the validity of the theoretical results.     

Robust exponential stability for discrete‐time interval BAM neural networks with delays and Markovian jump parameters

This paper investigates the problem of global robust exponential stability for discrete‐time interval BAM neural networks with mode‐dependent time delays and Markovian jump parameters, by utilizing the Lyapunov–Krasovskii functional combined with the linear matrix inequality (LMI) approach. A new Markov process as discrete‐time, discrete‐state Markov process is considered. An exponential stability performance analysis result is first established for error systems without ignoring any terms in the derivative of Lyapunov functional by considering the relationship between the time‐varying delay and its upper bound. The delay factor depends on the mode of operation. Three numerical examples are given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

This article mainly examine a class of robust synchronization, global stability criterion, and boundedness analysis for delayed fractional‐order competitive type‐neural networks with impulsive effects and different time scales. Firstly, by endowing the robust analysis skills and a new class of Lyapunov‐Krasovskii functional approach, the error dynamical system is furnished to be a robust adaptive synchronization in the voice of linear matrix inequality (LMI) technique. Secondly, by ignoring the uncertain parameter terms, the existence of equilibrium points are established by means of topological degree properties, and the solution representation of the considered network model are provided. Thirdly, a novel global asymptotic stability condition is proposed in the voice of LMIs, which is less conservative. Finally, our analytical results are justified with two numerical examples with simulations.     

Robust control of delayed Cohen–Grossberg neural networks

In this paper, robust control of Cohen–Grossberg neural networks with time delays is considered based on Lyapunov functional method and matrix inequality technique. Several new controllers with time delays and without time delays are designed to ensure the global asymptotic stability of equilibrium point, respectively. Finally, simulation examples are constructed to justify the proposed theoretical analysis. Copyright © 2007 John Wiley & Sons, Ltd.     

Comparison of convergence and stability properties for the state and output solutions of neural networks

A typical neuron cell is characterized by the state variable and the neuron output, which is obtained by passing the state through a nonlinear active device implementing the neuron activation. The paper introduces a wide class of neural networks for which the state solutions and the output solutions enjoy the same convergence and stability properties. The class, which includes as a special case the standard cellular neural networks, is characterized by piecewise‐linear Lipschitz continuous neuron activations, Lipschitz continuous (possibly) high‐order interconnections between neurons and asymptotically stable isolated neuron cells. The paper also shows that if we relax any of the assumptions on the smoothness of the neuron activations or interconnecting structure, or on the stability of the isolated neuron cells, then the equivalence between the convergence properties of the state solutions and the output solutions is in general no longer guaranteed. To this end, three relevant classes of neural networks in the literature are considered, where each class violates one of the assumptions made in the paper, and it is shown that the state solutions of the networks enjoy stronger convergence properties with respect to the output solutions or viceversa. Copyright © 2010 John Wiley & Sons, Ltd.     

Pseudomemories of two‐dimensional multistate hopfield neural networks

Complex‐valued Hopfield neural networks (CVHNNs) are available for storage of multilevel data, such as gray‐scale images. Such networks have low noise tolerance. This is a severe problem for their applications. To improve the noise tolerance, we have to study pseudomemories. In the case of one training pattern, CVHNNs have only rotated patterns as pseudomemories. There are many rotated patterns. This is considered the reason why CVHNNs have low noise tolerance. In the present paper, we investigate the pseudomemories of two‐dimensional multistate Hopfield neural networks, including the complex‐valued ones, with multiple training patterns. Computer simulations show that there are many pseudomemories other than the rotated patterns. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.