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. This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the National Natural Science Foundation of China under Grant 60774073, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the Natural Science Foundation of Jiangsu Education Committee of China under Grant 06KJD110206, the Scientific Innovation Fund of Yangzhou University of China under Grant 2006CXJ002, and the Alexander von Humboldt Foundation of Germany.     

Adaptive synchronization of stochastic neural networks with mixed time delays and reaction–diffusion terms

In this paper, the problem of exponential synchronization is investigated for a class of stochastic perturbed chaotic neural networks with both mixed time delays and reaction?Cdiffusion terms. By employing Lyapunov?CKrasovskii functional and stochastic analysis approaches, an adaptive controller is designed to guarantee the exponential synchronization of proposed neural networks in the mean square. In particular, the mixed time delays in this paper synchronously consist of constant delay in the leakage term (i.e., ??leakage delay??), discrete time-varying delay and distributed time-varying delay which are more general than those discussed in the previous literature. Furthermore, our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. Therefore, the results obtained in this paper generalize and improve those given in the previous literature. Finally, the extensive simulations are performed to show the effectiveness and feasibility of the obtained method.     

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.     

Stability criteria for periodic neural networks with discrete and distributed delays

In this paper, the stability analysis problem is dealt with for a class of periodic neural networks with both discrete and distributed time delays. Both global asymptotic and exponential stabilities are considered. The existence of the periodic solutions of the addressed neural networks is briefly discussed. Then, by constructing different Lyapnuov--Krasovskii functionals and using some analysis techniques, several new easy-to-test sufficient conditions are derived, respectively, for checking the globally asymptotic stability and globally exponential stability of the delayed neural networks. These results are useful in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for recurrent neural networks with mixed time delays. A simulation example is provided to demonstrate the effectiveness of the results obtained.     

State estimation for switched discrete-time stochastic BAM neural networks with time varying delay

This paper focuses the issue of state estimation for a class of switched discrete-time stochastic bidirectional associative memory (BAM) neural networks with time varying delay. The main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the error state system to be robustly exponentially stable. By employing average dwell time approach together with piecewise Lyapunov functional technique, a set of sufficient conditions is derived with respect to all admissible uncertainties, to guarantee the existence of the desired state estimator for the uncertain switched discrete-time BAM delayed neural networks. Specifically, we derive sufficient conditions to achieve robust state estimation with the characterization of complex effects of time delays, parameter uncertainties, and stochastic perturbations. In particular, the parameter uncertainties are assumed to be time varying and unknown, but norm bounded. It should be mentioned that our estimation results are delay dependent, which depend on not only the upper bounds of time delay, but also their lower bounds. More precisely, the desired estimator matrix gain is obtained in terms of the solution of the derived LMIs. Finally, numerical examples with a simulation result are given to illustrate the effectiveness and applicability of the obtained results.     

Exponential stability for switched Cohen–Grossberg neural networks with average dwell time

In this paper, uncertain switched Cohen–Grossberg neural networks with interval time-varying delay and distributed time-varying delay are proposed. Novel multiple Lyapunov functions are employed to investigate the stability of the switched neural networks under the switching rule with the average dwell time property. Sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) which guarantee the exponential stability for the switched Cohen–Grossberg neural networks. Numerical examples are provided to illustrate the effectiveness of the proposed method.     

Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters

In this paper, the stability analysis problem is considered for a class of stochastic neural networks with mixed time-delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays, and the jumping parameters are generated from a continuous-time discrete-state homogeneous Markov process. The aim of this paper is to establish some criteria under which the delayed stochastic neural networks are exponentially stable in the mean square. By constructing suitable Lyapunov functionals, several stability conditions are derived on the basis of inequality techniques and the stochastic analysis. An example is also provided in the end of this paper to demonstrate the usefulness of the proposed criteria.     

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated.A new stability condition is presented based on the Lyapunov-Krasovskii method,which is dependent on the amount of delay.A result is given in the form ofa linear matrix inequdlity,and the admitted upper bound of the delay can be easily obtained.The time delay dependent and independent results can be obtained,which include flome previously published resultS.A numerical example is given to show the effectiveness of the main results.     

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main 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.     

Adaptive synchronization of chaotic Cohen–Crossberg neural networks with mixed time delays

In this paper, the problem of adaptive synchronization is investigated for a class of Cohen–Crossberg neural networks with mixed time delays. Based on a Lyapunov–Krasovskii functional and the invariant principle of function differential equations as well as the adaptive control and linear feedback with update law, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving synchronization of the two coupled networks with mixed time delays. In particular, the mixed time delays in this paper synchronously consist of constant delays, time-varying delays, and distributed delays, which are more general than those discussed in the previous literature. Therefore, the results obtained in this paper comprise and generalize those given in the previous literature. A numerical example and its simulation are provided to show the effectiveness of the theoretical results.     

Input-to-state stability of impulsive reaction–diffusion neural networks with infinite distributed delays

In this paper, we focus on the global existence–uniqueness and input-to-state stability of the mild solution of impulsive reaction–diffusion neural networks with infinite distributed delays. First, the model of the impulsive reaction–diffusion neural networks with infinite distributed delays is reformulated in terms of an abstract impulsive functional differential equation in Hilbert space and the local existence–uniqueness of the mild solution on impulsive time interval is proven by the Picard sequence and semigroup theory. Then, the diffusion–dependent conditions for the global existence–uniqueness and input-to-state stability are established by the vector Lyapunov function and M-matrix where the infinite distributed delays are handled by a novel vector inequality. It shows that the ISS properties can be retained for the destabilizing impulses if there are no too short intervals between the impulses. Finally, three numerical examples verify the effectiveness of the theoretical results and that the reaction–diffusion benefits the input-to-state stability of the neural-network system.

     

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.     

Passivity analysis of stochastic time-delay neural networks

Passivity analysis of stochastic neural networks with time-varying delays and parametric uncertainties is investigated in this paper. Passivity of stochastic neural networks is defined. Both delay-independent and delay-dependent stochastic passivity conditions are presented in terms of linear matrix inequalities (LMIs). The results are established by using the Lyapunov–Krasovskii functional method. In order to derive the delay-dependent passivity criterion, some free-weighting matrices are introduced. The effectiveness of the method is illustrated by numerical examples.     

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...     

Synchronization error bound of chaotic delayed neural networks

Synchronization of master–slave chaotic neural networks are well studied through asymptotic and exponential stability of error dynamics. Besides qualitative properties of error dynamics, there is a need to quantify the error in real-time experiments especially in secure communication system. In this article, we focused on quantitative analysis of error dynamics by finding the exact analytical error bound for the synchronization of delayed neural networks. Using the Halanay inequality, the error bound is going to be obtained in terms of exponential of given system parameters and delay. The time-varying coupling delay has been considered in the neural networks which does not require any restrictive condition on the derivative of the delay. The proposed method can also be applied to find error bound for state estimation problem. The analytical synchronization bound has been corroborated by two examples.     

Passivity of uncertain neural networks with both leakage delay and time-varying delay

In this paper, the passivity problem is investigated for a class of uncertain neural networks with leakage delay and time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov–Krasovskii functionals, and employing Newton–Leibniz formulation and the free-weighting matrix method, several delay-dependent criteria for checking the passivity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.     

State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory

In this paper, the state estimation problem is investigated for neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. 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 is globally stable in the mean square and passive from the control input to the output error. Based on the new Lyapunov?CKrasovskii functional and passivity theory, delay-dependent conditions are obtained in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate effectiveness of the proposed method and 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.     

Switched exponential state estimation of neural networks based on passivity theory

In this paper, a new exponential state estimation method is proposed for switched Hopfield neural networks based on passivity theory. Through available output measurements, the main purpose is to estimate the neuron states such that the estimation error system is exponentially stable and passive from the control input to the output error. Based on augmented Lyapunov–Krasovskii functional, Jensen’s inequality, and linear matrix inequality (LMI), a new delay-dependent state estimator for switched Hopfield neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving delay-dependent LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.