Passivity analysis for neural networks with a time-varying delay

This paper deals with the problem of passivity analysis for neural networks with both time-varying delay and norm-bounded parameter uncertainties by employing an improved free-weighting matrix approach. Some useful terms have been retained, which were used to be ignored in the derivative of Lyapunov-Krasovskii functional. Furthermore, the relationship among the time-varying delay, its upper bound and their difference is taken into account. As a result, for two types of time-varying delays, less conservative delay-dependent passivity conditions are obtained in terms of linear matrix inequalities (LMIs), respectively. Finally, a numerical example is given to demonstrate the effectiveness of the proposed techniques.     

Delay-dependent robust asymptotic state estimation of Takagi-Sugeno fuzzy Hopfield neural networks with mixed interval time-varying delays

This paper investigates delay-dependent robust asymptotic state estimation of fuzzy neural networks with mixed interval time-varying delay. In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the robust state estimation of Hopfield neural networks with mixed interval time-varying delays. 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 is globally asymptotically stable. Based on the Lyapunov-Krasovskii functional which contains a triple-integral term, delay-dependent robust state estimation for such T-S fuzzy Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

New exponentially convergent state estimation method for delayed neural networks

The problem of designing a globally exponentially convergent state estimator for a class of delayed neural networks is investigated in this paper. The time-delay pattern is quite general and including fast time-varying delays. The activation functions are monotone nondecreasing with known lower and upper bounds. A linear estimator of Luenberger-type is developed and by properly constructing a new Lyapunov–Krasovskii functional coupled with the integral inequality, the global exponential stability conditions of the error system are derived. The unknown gain matrix is determined by solving a delay-dependent linear matrix inequality. The developed results are shown to be less conservative than previously published ones in the literature, which is illustrated by a representative numerical example.     

Ultimate boundedness of stochastic Hopfield neural networks with time-varying delays

By employing Lyapunov functional theory as well as linear matrix inequalities, ultimate boundedness of stochastic Hopfield neural networks (HNN) with time-varying delays is investigated. Sufficient criteria on ultimate boundedness of stochastic HNN are firstly obtained, which fills up a gap and includes deterministic systems as our special case. Finally, numerical simulations are presented to illustrate the correctness and effectiveness of our theoretical results.     

Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay

In this paper, we focus on the stability problem for discrete-time switched neural networks with time-varying delay resorting to the average dwell time method. In terms of linear matrix inequality approach, a delay-dependent sufficient condition of exponential stability is developed for a kind of switching signal with average dwell time. A numerical example is given to show the validness of the established result.     

New delay-dependent stability results for discrete-time recurrent neural networks with time-varying delay

This paper studies the problem of stability analysis for discrete-time recurrent neural networks (DRNNs) with time-varying delays. By using the discrete Jensen inequality and the sector bound conditions, a new less conservative delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs) under a weak assumption on the activation functions. By using a delay decomposition method, a further improved stability criterion is also derived. It is shown that the newly obtained results are less conservative than the existing ones. Meanwhile, the computational complexity of the newly obtained stability conditions is reduced since less variables are involved. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method.     

Improved delay-dependent stability criteria for neural networks with two additive time-varying delay components

In this paper, the problem of stability criteria of neural networks with two additive time-varying delay components is investigated. Some new delay-dependent stability criteria are derived in terms of linear matrix inequalities by choosing a new class of Lyapunov functional. The obtained criteria are less conservative because reciprocally convex approach and convex polyhedron approach are considered. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

New delay-dependent criterion for the stability of recurrent neural networks with time-varying delay

This paper is concerned with the global asymptotic stability of a class of recurrent neural networks with interval time-varying delay. By constructing a suitable Lyapunov functional, a new criterion is established to ensure the global asymptotic stability of the concerned neural networks, which can be expressed in the form of linear matrix inequality and independent of the size of derivative of time varying delay. Two numerical examples show the effectiveness of the obtained results. Supported by the National Natural Science Foundation of China (Grant Nos. 60534010, 60728307, 60774048, 60774093), the Program for Cheung Kong Scholars and Innovative Research Groups of China (Grant No. 60521003) and the National High-Tech Research & Development Program of China (Grant No. 2006AA04Z183), China Postdoctoral Sciencer Foundation (Grant No. 20080431150), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200801451096)     

State estimation for fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays

This paper deals with the problem of state estimation for fuzzy cellular neural networks (FCNNs) with time delay in the leakage term, discrete and unbounded distributed delays. In this paper, leakage delay in the leakage term is used to unstable the neuron states. It is challenging to develop a delay dependent condition to estimate the unstable neuron states through available output measurements such that the error-state system is globally asymptotically stable. By constructing the Lyapunov-Krasovskii functional which contains a triple-integral term, an improved delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). However, by using the free-weighting matrices method, a simple and efficient criterion is derived in terms of LMIs for estimation. The restriction such as the time-varying delay which was required to be differentiable or even its time-derivative which was assumed to be smaller than one, are removed. Instead, the time-varying delay is only assumed to be bounded. Finally, numerical examples and its simulations are given to demonstrate the effectiveness of the derived results.     

Less conservative results of state estimation for delayed neural networks with fewer LMI variables

In this paper, the state estimation problem is investigated for neural networks with time-varying delays as well as general activation functions. By applying the Finsler's Lemma and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent conditions are developed to estimate the neuron state with some available output measurements such that the error-state system is global asymptotically stable. It is established theoretically that one special case of the obtained criteria is equivalent to some existing result with same conservatism but including fewer LMI variables. As the present conditions involve no free-weighting matrices, the computational burden is largely reduced. Two examples are provided to demonstrate the effectiveness of the theoretical results.     

A delay decomposition approach to delay-dependent passivity analysis for interval neural networks with time-varying delay

This paper is concerned with delay-dependent passivity analysis for interval neural networks with time-varying delay. By decomposing the delay interval into multiple equidistant subintervals, new Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these new LKFs, a new passivity criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of the time delay. Finally, some numerical examples are given to illustrate the effectiveness of the developed techniques.     

Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays

The authors analyze the existence of the equilibrium point and global exponential stability for Hopfield reaction-diffusion neural networks with time-varying delays by means of the topological degree theory and generalized Halanay inequality. Since the diffusion phenomena and time delay could not be ignored in neural networks and electric circuits, the model presented here is close to the actual systems, and the sufficient conditions on global exponential stability established in this paper, which are easily verifiable, have a wider adaptive range.     

Guaranteed cost synchronization of chaotic cellular neural networks with time-varying delay

Synchronization of cellular neural networks with time-varying delay is discussed in this letter. Based on Razumikhin theorem, a guaranteed cost synchronous controller is given. Unlike Lyapunov-Krasovskii analysis process, there is no constraint on the change rate of time delay. The saturated terms emerging in the Razumikhin analysis are amplified by zoned discussion and maximax synthesis rather than by Lipschitz condition and vector inequality, which will bring more conservatism. Then the controller criterion is transformed from quadratic matrix inequality form into linear matrix inequality form, with the help of a sufficient and necessary transformation condition. The minimization of the guaranteed cost is studied, and a further criterion for getting the controller is presented. Finally, the guaranteed cost synchronous control and its corresponding minimization problem are illustrated with examples of chaotic time-varying delay cellular neural networks.     

Guaranteed cost synchronous control of time-varying delay cellular neural networks

This paper deals with the synchronization of time-varying delay cellular neural networks. Based on the Lyapunov stability analysis and the zoned discussion and maximax synthesis (ZDMS) method, the quadratic matrix inequality (QMI) criterion for the guaranteed cost synchronous controller is designed to synchronize the given chaotic systems. For the convenience to solve, using a generalized result of Schur complement, the criterion in the form of QMI is turned into the linear matrix inequality (LMI) form, which can be used efficiently via existing numerical convex optimization algorithms such as the interior-point algorithms for solving LMIs. The minimization of the guaranteed cost is further studied, and the corresponding LMI criterion for getting the controller is given. Finally, numerical examples are given to show the effectiveness of proposed guaranteed cost synchronous control and its corresponding minimization problem.     

Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay

In this paper, we consider the problem of global stabilization for a class of stochastic high-order feedforward nonlinear systems with time-varying delay. By introducing the homogeneous domination design method and constructing the appropriate Lyapunov–Krasovskii functional, a state feedback controller is constructed to drive the closed-loop system to be globally asymptotically stable in probability.     

An estimation of the domain of attraction for recurrent neural networks with time-varying delays

Based on Lyapunov–Krasovskii functional or Lyapunov–Razumikhin functional method and invariant set principle, we presented a new method to estimate the domain of attraction for general recurrent neural networks with time-varying delays. Convex optimization method is proposed to enlarge and estimate the domain of attraction. Local exponential stability conditions are derived, which can be expressed as linear matrix inequalities (LMIs) in terms of all the varying parameters and hence can be easily checked in both analysis and design.     

New stability criteria for BAM neural networks with time-varying delays

In this paper, the exponential stability is investigated for a class of time-delay BAM neural networks (NNs). Time delays of two layers are taken into account separately rather than as a whole with the idea of delay fractioning. Then we generalize the result to time-varying interval delay condition. Exploiting the known constant part of delay sufficiently to estimate the upper bounds, we can derive an improved stability for BAM NNs with time-varying interval delay. Two examples are provided to demonstrate the less conservatism and effectiveness of the proposed linear matrix inequality (LMI) conditions.     

Sensor selection strategies for state estimation in energy constrained wireless sensor networks

Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information over a shared channel to a central base station. The base station computes an estimate of the process state by means of a Kalman filter. In this paper we assume that, at each time step, only a subset of all sensors are selected to send their observations to the fusion center due to channel capacity constraints or limited energy budget. We propose a multi-step sensor selection strategy to schedule sensors to transmit for the next T steps of time with the goal of minimizing an objective function related to the Kalman filter error covariance matrix. This formulation, in a relaxed convex form, defines an unified framework to solve a large class of optimization problems over energy constrained WSNs. We offer some numerical examples to further illustrate the efficiency of the algorithm.     

Global robust passivity analysis for stochastic fuzzy interval neural networks with time-varying delays

In this paper, the problem of passivity analysis is investigated for uncertain stochastic fuzzy interval neural networks with time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. For the neural networks under study, a generalized activation function is considered, where the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique, new delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs), which can be solved by some standard numerical packages. Finally, numerical examples are given to show the effectiveness and merits of the proposed method.