Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates

In this paper, the problem of stochastic stability criterion of Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates is considered. Some new delay-dependent stability criteria are derived by choosing a new class of Lyapunov functional. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

State estimation for Markovian jumping genetic regulatory networks with random delays

In this paper, the state estimation problem is investigated for stochastic genetic regulatory networks (GRNs) with random delays and Markovian jumping parameters. The delay considered is assumed to be satisfying a certain stochastic characteristic. Meantime, the delays of GRNs are described by a binary switching sequence satisfying a conditional probability distribution. The aim of this paper is to design a state estimator to estimate the true states of the considered GRNs through the available output measurements. By using Lyapunov functional and some stochastic analysis techniques, the stability criteria of the estimation error systems are obtained in the form of linear matrix inequalities under which the estimation error dynamics is globally asymptotically stable. Then, the explicit expression of the desired estimator is shown. Finally, a numerical example is presented to show the effectiveness of the proposed results.     

New delay‐dependent global robust passivity analysis for stochastic neural networks with Markovian jumping parameters and interval time‐varying delays

The problem of passivity analysis for stochastic neural networks with Markovian jumping parameters and interval time‐varying delays is investigated in this article. By constructing a novel Lyapunov–Krasovskii functional based on the complete delay‐decomposing idea and using improved free‐weighting matrix method, some improved delay‐dependent passivity criteria are established in terms of linear matrix inequalities. Numerical examples are also given to show the effectiveness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 167–179, 2016     

Robust stability analysis of stochastic neural networks with Markovian jumping parameters and probabilistic time‐varying delays

This article discusses the issue of robust stability analysis for a class of Markovian jumping stochastic neural networks (NNs) with probabilistic time‐varying delays. The jumping parameters are represented as a continuous‐time discrete‐state Markov chain. Using the stochastic stability theory, properties of Brownian motion, the information of probabilistic time‐varying delay, the generalized Ito's formula, and linear matrix inequality (LMI) technique, some novel sufficient conditions are obtained to guarantee the stochastical stability of the given NNs. In particular, the activation functions considered in this article are reasonably general in view of the fact that they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. The main features of this article are described in the following: first one is that, based on generalized Finsler lemma, some improved delay‐dependent stability criteria are established and the second one is that the nonlinear stochastic perturbation acting on the system satisfies a class of Lipschitz linear growth conditions. By resorting to the Lyapunov–Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established using an efficient LMI approach. Finally, two numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–72, 2016     

Stability analysis of the differential genetic regulatory networks model with time-varying delays and Markovian jumping parameters

In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov–Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results.     

Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.     

Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays

In this paper, the stability analysis problem is investigated for a class of Markovian jumping genetic regulatory networks (GRNs) with mixed time delays (discrete time delays and distributed time delays) and stochastic perturbations. The main purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid and protein is asymptotically stable. By utilizing a more general Lyapunov-Krasovskii functional based on the idea of “delay decomposing” and the LMI (linear matrix inequality) technique, we derive sufficient delay-dependent conditions ensuring the asymptotically stability of the GRNs with mixed time delays and noise perturbations in terms of LMI. Finally, simulation examples are exploited to illustrate the effectiveness of the developed theoretical results.     

Exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays

This paper studies the problems of global exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential stability in the mean square for the reaction-diffusion high-order neural networks are established, which are easily verifiable and have a wider adaptive. An example is also discussed to illustrate our results.     

Master-slave synchronization of neural networks with time-varying delays via the event-triggered control

ABSTRACT

This paper investigates the problem of master-slave synchronization of neural networks with time-varying delays via the event-triggered control (ETC). First, the proposed ETC can effectively reduce the total amount of data transmitted to the controller in the synchronization process and avoid communication channel congestion. Second, a master-slave synchronization of neural networks with time-varying delays is constructed, where delays within neural networks and the ETC are simultaneous existence. The controller is updated by the ETC. By the Lyapunov stability theory, some sufficient criteria are obtained to ensure master-slave synchronization of neural networks. Finally, a numerical example and a tunnel diode circuit example are used to verify the validity of results obtained.     

Global exponential stability of impulsive discrete-time neural networks with time-varying delays

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria.     

Exponential stability analysis for uncertain neural networks with interval time-varying delays

In this paper, the problem of exponential stability analysis for neural networks is investigated. It is assumed that the considered neural networks have norm-bounded parametric uncertainties and interval time-varying delays. By constructing a new Lyapunov functional, new delay-dependent exponential stability criteria with an exponential convergence rate are established 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 effectiveness of proposed criteria.     

Delay decomposition approach to state estimation of neural networks with mixed time‐varying delays and Markovian jumping parameters

This paper investigates the state estimation of neural networks with mixed time‐varying delays and Markovian jumping parameters. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. On the basis of the new Lyapunov–Krasovskii functional, some inequality techniques, stochastic stability theory and delay‐dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, three numerical examples are given to illustrate the less conservative and effectiveness of our theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

Delay-range dependent stability criteria for neural networks with Markovian jumping parameters

The paper is concerned with a stability analysis problem for neural networks with Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process, which are governed by a Markov process with discrete and finite state space. A new type of Markovian jumping matrix P_i is introduced in this paper. The discrete delays are 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, a numerical example is provided to demonstrate the lower conservatism and the effectiveness of the proposed LMI conditions.     

Adaptive synchronization of Cohen-Grossberg neural networks with unknown parameters and mixed time-varying delays

In this paper, we investigate the synchronization problem of chaotic Cohen-Grossberg neural networks with unknown parameters and mixed time-varying delays. An adaptive linear feedback controller is designed to guarantee that the response system can be synchronized with a drive system by utilizing Lyapunov stability theory and parameter identification. Our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. These results generalize a few previous known results and remove some restrictions on amplification function and time delay. This research also demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.     

Exponential stability for markovian jumping stochastic BAM neural networks with mode‐dependent probabilistic time‐varying delays and impulse control

In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode‐dependent probabilistic time‐varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time‐varying delay is considered and transformed into one with deterministic time‐varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov‐Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple‐integral term is introduced for deriving the delay‐dependent stability conditions. Furthermore, mode‐dependent mean square exponential stability criteria are derived by constructing a new Lyapunov‐Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 39–65, 2015     

Robust asymptotic state estimation of Takagi–Sugeno fuzzy Markovian jumping Hopfield neural networks with mixed interval time‐varying delays

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the state estimation of uncertain Markovian jumping 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 are globally asmptotically stable in the mean square. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, several delay‐dependent robust state estimators for such T–S fuzzy Markovian jumping Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. Finally a numerical example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Exponential synchronization of Markovian jumping chaotic neural networks with sampled-data and saturating actuators

This paper deals with the problem of exponential synchronization of Markovian jumping chaotic neural networks with saturating actuators using a sampled-data controller. By constructing a proper Lyapunov–Krasovskii functional (LKF) with triple integral terms, and employing Jensen’s inequality, some new sufficient conditions for the exponential synchronization of considered chaotic neural networks are derived in terms of linear matrix inequalities (LMIs). The obtained LMIs can be easily solved by any of the available software. Finally, the numerical examples are provided to demonstrate the effectiveness of our theoretical results.     

Passivity analysis of neural networks with Markovian jumping parameters and interval time-varying delays

In this paper, the problem of passivity analysis is investigated for neural networks with Markovian jumping parameters, interval time-varying delays and norm bounded parameter uncertainties. The delay-dependent passivity conditions are derived for two types of interval time-varying delay in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are given to show the effectiveness of the proposed conditions.     

On exponential stability analysis for neural networks with time-varying delays and general activation functions

This paper is concerned with the exponential stability analysis for a class of cellular neural networks with both interval time-varying delays and general activation functions. The boundedness assumption of the activation function is not required. The limitation on the derivative of time delay being less than one is relaxed and the lower bound of time-varying delay is not restricted to be zero. A new Lyapunov-Krasovskii functional involving more information on the state variables is established to derive a novel exponential stability criterion. The obtained condition shows potential advantages over the existing ones since no useful item is ignored throughout the estimate of upper bound of the derivative of Lyapunov functional. Finally, three numerical examples are included to illustrate the proposed design procedures and applications.