Stability of stochastic Markovian jump neural networks with mode-dependent delays

In this paper, the problem of stability analysis for a general class of uncertain stochastic neural networks with Markovian jumping parameters and mixed mode-dependent delays is considered. By the use of a new Markovian switching Lyapunov–Krasovskii functional, delay-dependent conditions on mean square asymptotic stability are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed approach.     

Stability results for Takagi–Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time delays in the leakage term by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of BAM neural networks with time-varying delays. The parameter uncertainties are assumed to be norm bounded. Some new delay-dependent stability conditions are derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Even there is no leakage delay, the obtained results are also less restrictive than some recent works. It can be applied to BAM neural networks with activation functions without assuming their boundedness, monotonicity, or differentiability. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

     

Exponential convergence rate estimation for neutral BAM neural networks with mixed time-delays

This paper is concerned with the exponential stability analysis problem for a class of neutral bidirectional associative memory neural networks with mixed time-delays, where discrete, distributed and neutral delays are involved. By utilizing the delay decomposition approach and an appropriately constructed Lyapunov–Krasovskii functional, some novel delay-dependent and decay rate-dependent criteria for the exponential stability of the considered neural networks are derived and presented in terms of linear matrix inequalities. Furthermore, the maximum allowable decay rate can be estimated based on the obtained results. Three numerical examples are given to demonstrate the effectiveness of the proposed method.     

New LMT-based delay-dependent criterion for global asymptotic stability of cellular neural networks

The problem of global asymptotic stability analysis is studied for a class of cellular neural networks with time-varying delay. By defining a Lyapunov–Krasovskii functional, a new delay-dependent stability condition is derived in terms of linear matrix inequalities. The obtained criterion is less conservative than some previous literature because free-weighting matrix method and the Jensen integral inequality are considered. Three illustrative examples are given to demonstrate the effectiveness of the proposed results.     

Stability analysis of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays.

This correspondence investigates the global exponential stability problem of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays (TSFDCNNs). Based on the Lyapunov-Krasovskii functional theory and linear matrix inequality technique, a less conservative delay-dependent stability criterion is derived to guarantee the exponential stability of TSFDCNNs. By constructing a Lyapunov-Krasovskii functional, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is released in the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the effectiveness of the proposed results.     

Stability Analysis of Takagi–Sugeno Fuzzy Cellular Neural Networks With Time-Varying Delays

This correspondence investigates the global exponential stability problem of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays (TSFDCNNs). Based on the Lyapunov-Krasovskii functional theory and linear matrix inequality technique, a less conservative delay-dependent stability criterion is derived to guarantee the exponential stability of TSFDCNNs. By constructing a Lyapunov-Krasovskii functional, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is released in the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the effectiveness of the proposed results     

Novel robust stability criteria of discrete-time stochastic recurrent neural networks with time delay

The problem of robust global exponential stability is investigated for a class of stochastic uncertain discrete-time recurrent neural networks with time delay. In this paper, the midpoint of the time delay's variation interval is introduced, and the variation interval is divided into two subintervals. Then, by constructing a new Lyapunov–Krasovskii functional and checking its variation in the two subintervals, respectively, some novel delay-dependent stability criteria for the addressed neural networks are derived. Numerical examples are provided to show that the achieved conditions are less conservative than some existing ones in the literature.     

Almost Sure Exponential Stability of Recurrent Neural Networks With Markovian Switching

This paper presents new stability results for recurrent neural networks with Markovian switching. First, algebraic criteria for the almost sure exponential stability of recurrent neural networks with Markovian switching and without time delays are derived. The results show that the almost sure exponential stability of such a neural network does not require the stability of the neural network at every individual parametric configuration. Next, both delay-dependent and delay-independent criteria for the almost sure exponential stability of recurrent neural networks with time-varying delays and Markovian-switching parameters are derived by means of a generalized stochastic Halanay inequality. The results herein include existing ones for recurrent neural networks without Markovian switching as special cases. Finally, simulation results in three numerical examples are discussed to illustrate the theoretical results.     

Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities

This paper addresses the problems of stability and synchronization for a class of Markovian jump neural networks with partly unknown transition probabilities. We first study the stability analysis problem for a single neural network and present a sufficient condition guaranteeing the mean square asymptotic stability. Then based on the Lyapunov functional method and the Kronecker product technique, the chaos synchronization problem of an array of coupled networks is considered. Both the stability and the synchronization conditions are delay-dependent, which are expressed in terms of linear matrix inequalities. The effectiveness of the developed methods is shown by simulation examples.     

Stochastic stability of Markovian jumping Hopfield neural networks with constant and distributed delays

This paper investigates the problem of stability analysis for Markovian jumping Hopfield neural networks (MJHNNs) with constant and distributed delays. Some new delay-dependent stochastic stability criteria are derived based on a novel Lyapunov–Krasovskii functional (LKF) approach. These new criteria based on the delay partitioning idea prove to be less conservative, since the conservatism could be notably reduced by thinning the delay partitioning. Numerical examples are provided to show the effectiveness and advantage of the proposed techniques.     

New stability analysis for generalized neural networks with interval time-varying delays

This paper deals with the problem of delay-dependent stability for neural networks with interval time-varying delays. First, we divided delay interval into two parts. Second, a new Lyapunov-Krasovskii functional is constructed, and relationships between the augmented state vectors have been fully considered, which may yield less conservative results. Third, based on free-matrix-based integral inequality method and reciprocally convex technique, some new less conservative delay-dependent stability criteria have been obtained by combining with the new Lyapunov-Krasovskii functional. Finally, two numerical examples are given to show the effectiveness of the derived conditions over the existing ones.     

Stability of uncertain impulsive stochastic fuzzy neural networks with two additive time delays in the leakage term

This paper is concerned with the stability problem for a class of impulsive neural networks model, which includes simultaneously parameter uncertainties, stochastic disturbances and two additive time-varying delays in the leakage term. By constructing a suitable Lyapunov–Krasovskii functional that uses the information on the lower and upper bound of the delay sufficiently, a delay-dependent stability criterion is derived by using the free-weighting matrices method for such Takagi–Sugeno fuzzy uncertain impulsive stochastic recurrent neural networks. The obtained conditions are expressed with linear matrix inequalities (LMIs) whose feasibility can be checked easily by MATLAB LMI Control toolbox. Finally, the theoretical result is validated by simulations.     

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.     

Delay-Dependent Stability for Recurrent Neural Networks With Time-Varying Delays

This brief is concerned with the stability for static neural networks with time-varying delays. Delay-independent conditions are proposed to ensure the asymptotic stability of the neural network. The delay-independent conditions are less conservative than existing ones. To further reduce the conservatism, delay-dependent conditions are also derived, which can be applied to fast time-varying delays. Expressed in linear matrix inequalities, both delay-independent and delay-dependent stability conditions can be checked using the recently developed algorithms. Examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result.      

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

This paper focuses on the problem of delay-dependent robust stability analysis for a class of uncertain stochastic neural networks with time-varying delay by employing improved free-weighting matrix method. Taking the relationship among the time-varying delay, its upper bound and their difference into account and using It[^(o)]'s\hbox{It}\hat{o}\hbox{'s} differential formula, some improved LMI-based delay-dependent stability criteria for stochastic neural networks are obtained without ignoring any terms, which guarantee systems globally robustly stochastically stable in the mean square. Finally, three numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.     

一类含有时变时滞的不确定中立型Hopfield神经网络的鲁棒稳定性判据

针对一类不确定中立型时变时滞Hopfield神经网络的鲁棒稳定性问题, 构造了一个新Lyapunov-Krasovskii泛函, 并结合自由矩阵方法和牛顿—莱布尼茨公式, 得到了新的时滞相关稳定性判据. 该判据考虑了中立型时变时滞Hopfield神经网络中的参数不确定性, 所得结果以线性矩阵不等式(Linear matrix inequality, LMI)的形式给出, 容易验证. 最后, 通过两个数值算例验证了该结果的有效性及可行性. 该判据对丰富与完善中立型神经网络的稳定性理论体系, 具有积极的意义.     

Robust Control of Uncertain Stochastic Recurrent Neural Networks with Time-varying Delay

In this paper, robust control of uncertain stochastic recurrent neural networks with time-varying delay is considered. A novel control method is given by using the Lyapunov functional method and linear matrix inequality (LMI) approach. Several delay-independent and delay-dependent sufficient conditions are then further derived to ensure the global asymptotical stability in mean square for the uncertain stochastic recurrent neural networks, and the estimation gains can also be obtained. Numerical examples are constructed to verify the theoretical analysis in this paper.     

Complete delay-decomposing approach to exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays

This paper considers the problem of exponential stability of uncertain cellular neural networks with discrete and distribute time-varying delays. Some new delay-dependent stability condition are derived in terms of linear matrix inequality. We divide delay interval into multiple segments and employ the free-weighting matrices method to obtained some less conservative criteria. Finally, numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Further results on delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays and Markovian jump parameters

This paper studies the problem of the robustly exponential stability of uncertain stochastic neural networks with mixed delays and Markovian jump parameters. In terms of linear matrix inequalities approach, some new delay-dependent stability criteria are established for the considered systems by constructing a modified Lyapunov–Krasovskii functional. And our derived results shown by three illustrative examples are more effective than some existing ones.

     

Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time-varying interval delays and Markovian jumping parameters by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of Markovian jumping BAM neural networks with time-varying interval delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite-state space. The new type of Markovian jumping matrices P_k and Q_k are introduced in this paper. The parameter uncertainties are assumed to be norm bounded and the 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. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Numerical examples are given to demonstrate the effectiveness of the proposed methods.