New delay-dependent stability criteria for neural networks with time-varying interval delay

The problem of stability analysis of neural networks with time-varying delay in a given range is investigated in this Letter. By introducing a new Lyapunov functional which uses the information on the lower bound of the delay sufficiently and an augmented Lyapunov functional which contains some triple-integral terms, some improved delay-dependent stability criteria are derived using the free-weighting matrices method. Numerical examples are presented to illustrate the less conservatism of the obtained results and the effectiveness of the proposed method.     

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

This paper studies the problem of linear matrix inequality (LMI) approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach,the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional,some inequality techniques and stochastic stability theory,new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism,which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally,numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.     

New asymptotic stability criteria for neural networks with time-varying delay

The problem of delay-dependent asymptotic stability criteria for neural networks with time-varying delay is investigated. A new class of Lyapunov functional is constructed to derive some new delay-dependent stability criteria.The obtained criterion are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.     

Novel delay-distribution-dependent stability analysis for continuous-time recurrent neural networks with stochastic delay

<正>In this paper,the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks(CRNNs) with stochastic delay.Different from the common assumptions on time delays,it is assumed that the probability distribution of the delay taking values in some intervals is known a priori.By making full use of the information concerning the probability distribution of the delay and by using a tighter bounding technique(the reciprocally convex combination method),less conservative asymptotic mean-square stable sufficient conditions are derived in terms of linear matrix inequalities(LMIs).Two numerical examples show that our results are better than the existing ones.     

Robust stability analysis for Markovian jumping stochastic neural networks with mode-dependent time-varying interval delay and multiplicative noise

This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks (MJSNNs) subject to mode-dependent time-varying interval delay and state-multiplicative noise. Based on the Lyapunov--Krasovskii functional and a stochastic analysis approach, some new delay-dependent sufficient conditions are obtained in the linear matrix inequality (LMI) format such that delayed MJSNNs are globally asymptotically stable in the mean-square sense for all admissible uncertainties. An important feature of the results is that the stability criteria are dependent on not only the lower bound and upper bound of delay for all modes but also the covariance matrix consisting of the correlation coefficient. Numerical examples are given to illustrate the effectiveness.     

Novel delay dependent stability analysis of Takagi—Sugeno fuzzy uncertain neural networks with time varying delays

This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi-Sugeno (T-S) model. The main results given here focus on the stability criteria using a new Lyapunov functional. New relaxed conditions and new linear matrix inequality-based designs are proposed that outperform the previous results found in the literature. Numerical examples are provided to show that the achieved conditions are less conservative than the existing ones in the literature.     

New results on stability criteria for neural networks with time-varying delays

In this paper,the problem of stability analysis for neural networks with time-varying delays is considered.By constructing a new augmented Lyapunov-Krasovskii’s functional and some novel analysis techniques,improved delaydependent criteria for checking the stability of the neural networks are established.The proposed criteria are presented in terms of linear matrix inequalities(LMIs) which can be easily solved and checked by various convex optimization algorithms.Two numerical examples are included to show the superiority of our results.     

Robust stability analysis of Takagi-Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays

In this paper,the global stability of Takagi-Sugeno (TS) uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays (TSUSFRNNs) is considered.A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs.The proposed stability conditions are demonstrated through numerical examples.Furthermore,the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed.Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.     

Improved delay-dependent globally asymptotic stability of delayed uncertain recurrent neural networks with Markovian jumping parameters

In this paper, we have improved delay-dependent stability criteria for recurrent neural networks with a delay varying over a range and Markovian jumping parameters. The criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism. In addition, a numerical example is provided to illustrate the applicability of the result using the linear matrix inequality toolbox in MATLAB.     

A delay-decomposition approach for stability of neural network with time-varying delay

This paper studies delay-dependent asymptotical stability problems for the neural system with time-varying delay. By dividing the whole interval into multiple segments such that each segment has a different Lyapunov matrix, some improved delay-dependent stability conditions are derived by employing an integral equality technique. A numerical example is given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

The global stability problem of Takagi-Sugeno(T-S) fuzzy Hopfield neural networks(FHNNs) with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler’s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.     

Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays

This Letter investigates the problem of delay-dependent exponential stability analysis for uncertain stochastic neural networks with time-varying delay. Based on the Lyapunov stability theory, improved delay-dependent exponential stability criteria for the networks are established in terms of linear matrix inequalities (LMIs).     

Synchronization criteria for coupled Hopfield neural networks with time-varying delays

This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov-Krasovskii's functional and use of Finsler's lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Improved stability criteria for neural networks with time-varying delay

The problem of the stability analysis of neural networks with time-varying delay is considered in this Letter. By constructing a new augmented Lyapunov functional which contains a triple-integral term, an improved delay-dependent stability criterion is derived in terms of LMI using the free-weighting matrices method. The rate-range of the delay is also considered in the derivation of the criterion. Numerical examples are presented to illustrate the effectiveness of the proposed method.     

Stability analysis of Markovian jumping stochastic Cohen Grossberg neural networks with discrete and distributed time varying delays

In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays （MJSCGNNs） is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen-Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples.     

Novel global robust stability criteria for interval neural networks with multiple time-varying delays

This Letter is concerned with the problem of robust stability analysis for interval neural networks with multiple time-varying delays and parameter uncertainties. The parameter uncertainties are assumed to be bounded in given compact sets and the activation functions are supposed to be bounded and globally Lipschitz continuous. A sufficient condition is obtained by means of Lyapunov functionals, which guarantees the existence, uniqueness and global asymptotic stability of the delayed neural network for all admissible uncertainties. This condition is in terms of a linear matrix inequality (LMI), which can be easily checked by using recently developed algorithms in solving LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

New synchronization analysis for complex networks with variable delays

This paper deals with the issue of synchronization of delayed complex networks. Differing from previous results,the delay interval [0,d(t)] is divided into some variable subintervals by employing a new method of weighting delays. Thus,new synchronization criteria for complex networks with time-varying delays are derived by applying this weighting-delay method and introducing some free weighting matrices. The obtained results have proved to be less conservative than previous results. The sufficient conditions of asymptotical synchronization are derived in the form of linear matrix inequality,which are easy to verify. Finally,several simulation examples are provided to show the effectiveness of the proposed results.     

Exponential passivity of neural networks with time-varying delay and uncertainty

In this Letter, delay-dependent exponential passivity condition for delayed neural networks is obtained. Then, the result is extended to two types of uncertainties. Two numerical examples are given to demonstrate the effectiveness of the proposed criteria.     

Exponential stability of cellular neural networks with multiple time delays and impulsive effects

In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality （LMI） and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.     

Combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and disturbances

In this paper, the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied. Firstly, the definition of combination projection synchronization of fractional-order complex dynamic networks is given, and the synchronization problem of the drive-response systems is transformed into the stability problem of the error system. In addition, time-varying delays and disturbances are taken into consideration to make the network synchronization more practical and universal. Then, based on Lyapunov stability theory and fractional inequality theory, the adaptive controller is formulated to make the drive and response systems synchronization by the scaling factors. The controller is easier to realize because there is no time-delay term in the controller. At last, the corresponding simulation examples demonstrate the effectiveness of the proposed scheme.