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.     

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.     

Observer design for neutral‐type neural networks with discrete and distributed time‐varying delays

This paper is concerned with the problem of state estimation for a class of neural networks with discrete and distributed interval time‐varying delays. We propose a new approach of nonlinear estimator design for the class of neutral‐type neural networks. By constructing a newly augmented Lyapunov‐Krasovskii functional, we establish sufficient conditions to guarantee the estimation error dynamics to be globally exponentially stable. The obtained results are formulated in terms of linear matrix inequalities (LMIs), which can be easily verified by the MATLAB LMI control toolbox. Then, the desired estimators gain matrix is characterized in terms of the solution to these LMIs. Three numerical examples are given to show the effectiveness of the proposed design method.     

Novel stability criteria of Cohen–Grossberg neural networks with time‐varying delays

In this paper, a class of Cohen–Grossberg neural networks with time‐varying delays is investigated. Based on several new Lyapunov–Krasovskii functionals, by employing the homeomorphism mapping principle, the Halanay inequality, a nonlinear measure approach and linear matrix inequality techniques, several delay‐independent sufficient criteria are obtained for the existence, uniqueness and globally exponential stability of considered neural networks. Without assuming the boundedness and monotonicity of activation functions, the obtained conditions generalize some previous results in the literature. Two examples are also given to show the less conservativeness of the obtained conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Enhanced result on stability analysis of randomly occurring uncertain parameters,leakage, and impulsive BAM neural networks with time‐varying delays: Discrete‐time case

In real‐world problems, neural networks play an increasingly important role in terms of both theory and applications. In this paper, the asymptotic stability analysis issue is investigated for uncertain impulsive discrete‐time bidirectional associative memory neural networks with leakage and time‐varying delays. With the assistance of novel summation inequality, reciprocally convex combination technique, and triple Lyapunov‐Krasovskii functionals terms, many cases of time‐varying delays are examined to certify the stability of neural networks. Here, the uncertainties are considered as a randomly occurring parameter uncertainty, and it conforms certain mutually uncorrelated Bernoulli‐distributed white noise sequences. An important feature of the results reported here is that the probability of occurrence of the parameter uncertainties specify a priori estimate. Finally, numerical examples are proposed to expose the capability and efficiency of our research work with the help of the LMI control toolbox in MATLAB.     

Adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems with input delays and state time‐varying delays

In this paper, an adaptive fuzzy backstepping dynamic surface control (DSC) approach is developed for a class of MIMO nonlinear systems with input delays and state time‐varying delays. The unknown continuous nonlinear functions are expressed as the linearly parameterized form by using the fuzzy logic systems, and then, by combining the backstepping technique, the appropriate Lyapunov–Krasovskii functionals, and the ‘minimal learning parameters’ algorithms with the DSC approach, the adaptive fuzzy tracking controller is designed. Our development is able to eliminate the problem of ‘explosion of complexity’ inherent in the existing backstepping‐based methods. It is proven that the proposed design method can guarantee that all the signals in the closed‐loop system are bounded and the tracking error is smaller than a prescribed error bound. Finally, simulation results are provided to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Sliding mode control of switched hybrid systems with time‐varying delay

This paper is concerned with the sliding mode control of a continuous‐time switched system with time‐varying delay in its state. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the exponential stability of the unforced system with the decay estimate explicitly given. A sufficient condition of the existence of a reduced‐order sliding mode dynamics is derived, and an explicit parametrization of the desired sliding surface is also given. The obtained conditions will be solved using the cone complementary linearization (CCL) method. An adaptive sliding mode controller for the reaching motion is then designed such that the trajectories of the resulting closed‐loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. All the conditions obtained in this paper are delay dependent. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theory. Copyright © 2008 John Wiley & Sons, Ltd.     

Decentralized adaptive robust stabilization of uncertain interconnected time‐delay systems

This paper considers the problem of decentralized adaptive robust stabilization of a class of interconnected time‐delay systems with arbitrarily bounded matched but limitedly bounded unmatched uncertainties. A new class of decentralized adaptive controllers based on Lyapunov–Krasovskii functional is proposed that guarantees bounded stability of the system and ensures nonfragileness of the controller to perturbations in its nonadaptive gain factor. The existence of such controllers is formulated in the LMI framework besides being presented using the Algebraic Riccati Equations. A numerical example is considered to illustrate the applicability and effectiveness of the proposed controller. Copyright © 2011 John Wiley & Sons, Ltd.     

Stability analysis and adaptive control for nonlinear discrete‐time systems with time delays and dead zone via state‐feedback technique

This research addresses the stability analysis and adaptive state‐feedback control for a class of nonlinear discrete‐time systems with multiple interval time‐varying delays and symmetry dead zone. The multiple interval time‐varying delays and symmetry dead zone are considered in the nonlinear discrete‐time system. The multiple interval time‐varying delays are bounded by the nonlinear function with unknown coefficients, and the symmetry dead zone is considered without the knowledge of the dead zone parameters. The adaptive state‐feedback controller is designed for the nonlinear discrete‐time systems with multiple interval time‐varying delays and dead zone. The discrete Lyapunov‐Krasovskii functional is introduced, such that the solutions of the closed‐loop error system converge to an adjustable bounded region and the state errors can be rendered arbitrarily small by adjusting the adaptive parameters. The designed adaptive state‐feedback controller does not require the knowledge of maximum and minimum values for the characteristic slopes of the dead zone. Finally, three simulation examples are given to show the effectiveness of the proposed methods.     

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.     

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

This paper considers the problem of adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H_∞ controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H_∞ performance of the closed‐loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

In this paper, an adaptive dynamic surface control approach is developed for a class of multi‐input multi‐output nonlinear systems with unknown nonlinearities, bounded time‐varying state delays, and in the presence of time‐varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some time‐varying values where the values, times, and patterns of the failures are unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. With the help of neural networks to approximate the unknown nonlinear functions and combining the dynamic surface control approach with the backstepping design method, a novel control approach is constructed. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed‐loop signals is guaranteed, and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark as well as a chemical reactor system. The simulation results show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Synchronization in nonlinear complex networks with multiple time‐varying delays via adaptive aperiodically intermittent control

This article is concerned with the problem of synchronization in nonlinear complex networks with multiple time‐varying delays via adaptive aperiodically intermittent control. The couplings inside nodes are assumed to be nonlinear and subject to multiple time‐varying delays. Meanwhile, the connection topology among the nodes can be directed and weighted. Then, the adaptive aperiodically intermittent control method is employed to realize synchronization and automatic modification to compensate the changes in dynamic errors. In addition, several synchronization criteria are rigorously induced based on the Lyapunov stability theory. Finally, the proposed control method is evaluated by utilizing numerical simulation. The results can be also applied to linear complex networks with delays.     

Pinning control and adaptive control for synchronization of linearly coupled reaction‐diffusion neural networks with mixed delays

This paper focuses on the pinning control and adaptive control for synchronization of an array of linearly coupled reaction‐diffusion neural networks with mixed delays (that is, discrete and infinite distributed delays) and Dirichlet boundary condition. Firstly, the asymptotical synchronization of coupled semilinear diffusion partial differential equations with mixed time delays is achieved by employing pinning control scheme. The pinning controller is obtained by using Lyapunov‐Krasovskii functional stability theory. The stability condition is represented by linear matrix inequality. The controller gain matrix is easy to be solved. Secondly, the adaptive synchronization condition of an array of linearly coupled reaction‐diffusion neural networks with mixed delays is obtained by using adaptive control scheme. Finally, two numerical examples of coupled semilinear diffusion partial differential equations with mixed time delays are given to illustrate the correctness of the obtained results.     

Mittag‐Leffler state estimator design and synchronization analysis for fractional‐order BAM neural networks with time delays

This paper deals with the extended design of Mittag‐Leffler state estimator and adaptive synchronization for fractional‐order bidirectional associative memory neural networks with time delays. By the aid of Lyapunov direct approach and Razumikhin‐type method, a suitable fractional‐order Lyapunov functional is constructed and a new set of novel sufficient condition are derived to estimate the neuron states via available output measurements such that the ensuring estimator error system is globally Mittag‐Leffler stable. Then, the adaptive feedback control rule is designed, under which the considered FBNNs can achieve Mittag‐Leffler adaptive synchronization by means of some fractional‐order inequality techniques. Moreover, the adaptive feedback control may be utilized even when there is no ideal information from the system parameters. Finally, two numerical simulations are given to reveal the effectiveness of the theoretical consequences.     

Gradient descent learning rule for complex‐valued associative memories with large constant terms

Complex‐valued associative memories (CAMs) are one of the most promising associative memory models by neural networks. However, the low noise tolerance of CAMs is often a serious problem. A projection learning rule with large constant terms improves the noise tolerance of CAMs. However, the projection learning rule can be applied only to CAMs with full connections. In this paper, we propose a gradient descent learning rule with large constant terms, which is not restricted by network topology. We realize large constant terms by regularization to connection weights. By computer simulations, we prove that the proposed learning algorithm improves noise tolerance. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

H∞ filtering for continuous‐time singular systems with time‐varying delay

This paper focuses on H_∞ filter design for continuous‐time singular systems with time‐varying delay. A delay‐dependent H_∞ performance analysis result is first established for error systems via a novel estimation method. By combining a well‐known inequality with a delay partition technique, the upper bound of the derivative of the Lyapunov functional is estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. Based on the derived H_∞ performance analysis results, a regular and impulse‐free H_∞ filter is designed in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Convergence of discrete‐time cellular neural networks with interlaced block‐sequential dynamics

Some interlaced block‐sequential modes of operation are introduced for discrete‐time cellular neural networks (DTCNN), and the corresponding convergence conditions are investigated. It is proved that DTCNNs, under some block‐sequential updating rules, result to be convergent when the feedback templates satisfy some restrictions rather milder than reciprocity or dominance, as required in synchronous mode. Moreover, the set of fixed points of the network results to be independent of the particular updating rule adopted. The drawback of desynchronization is a reduced speed of convergence, which however is tolerable in the usual case when the neighbourhood radius is small. Copyright © 1999 John Wiley & Sons, Ltd.