Robust exponential stability analysis of discrete-time switched Hopfield neural networks with time delay

The robust exponential stability problem in this paper for discrete-time switched Hopfield neural networks with time delay and uncertainty is considered. Firstly, the mathematical model of the system is established. Then by constructing a new Lyapunov–Krasovskii functional, some new delay-dependent criteria are developed, which guarantee the robust exponential stability of discrete-time switched Hopfield neural networks. A numerical example is provided to demonstrate the potential and effectiveness of the results obtained.     

Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays

This paper investigates delay-dependent robust exponential state estimation of Markovian jumping fuzzy neural networks with mixed random time-varying delay. In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the robust exponential state estimation of Markovian jumping Hopfield neural networks with mixed random time-varying delays. Moreover probabilistic delay satisfies a certain probability-distribution. By introducing a stochastic variable with a Bernoulli distribution, the neural networks with random time delays is transformed into one with deterministic delays and stochastic parameters. 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 exponentially 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. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally some numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Exponential stability criteria for discrete-time recurrent neural networks with time-varying delay

In this paper, the robust global exponential stability is investigated for the discrete-time recurrent neural networks (RNNs) with time-varying interval delay. By choosing an augmented Lyapunov–Krasovskii functional, delay-dependent results guaranteeing the global exponential stability and the robust exponential stability of the concerned neural network are obtained. The results are shown to be a generalization of some previous results, and less conservative than the existing works. Two numerical examples are given to demonstrate the applicability of the proposed method.     

Global robust exponential stability of delayed neural networks: An LMI approach

In this paper, the problems of determining the robust exponential stability and estimating the exponential convergence rate for neural networks with parametric uncertainties and time delay are studied. Based on Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique, some delay-dependent criteria are derived to guarantee global robust exponential stability. The exponential convergence rate can be easily estimated via these 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.     

Robust exponential stability of Markovian jumping neural networks with mode-dependent delay

This paper deals with the robust exponential stability problem for a class of Markovian jumping neural networks with time delay. The delay considered varies randomly, depending on the mode of the networks. By using a new Lyapunov–Krasovskii functional, a delay-dependent stability criterion is presented, which can be expressed in terms of linear matrix inequalities (LMIs). A numerical example is given to show the effectiveness of the results.     

A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays

In this paper, the problem of exponential passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing new augmented Lyapunov-Krasovskii’s functionals and some novel analysis techniques, improved delay-dependent criteria for checking the exponential passivity of the neural networks are established. The proposed criteria are represented in terms of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. A numerical example is included to show the superiority of our results.     

Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays

In this paper, the global exponential stability is investigated for a class of stochastic interval neural networks with time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. Based on Lyapunov stable theory and stochastic analysis approaches, the delay-dependent criteria are derived to ensure the global, robust, exponential stability of the addressed system in the mean square. The criteria can be checked easily by the LMI control toolbox in Matlab. A numerical example is given to illustrate the effectiveness and improvement over some existing results.     

New delay-dependent global robust stability conditions for interval neural networks with time-varying delays

This paper deals with the problem of delay-dependent global robust stability analysis for interval neural networks with time-varying delays. By introducing an equivalent transformation of interval systems and the free-weighting matrix technique, a new delay-dependent condition on global robust stability is established. This condition is presented in terms of a linear matrix inequality (LMI), which can be easily checked by using recently developed algorithms in solving LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

Delay-range-dependent robust H filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters

This paper investigates the problem of robust H^∞ filtering for uncertain stochastic time-delay systems with Markovian jump parameters. Both the state dynamics and measurement of the system are corrupted by Wiener processes. The time delay varies in an interval and depends on the mode of operation. A Markovian jump linear filter is designed to guarantee robust exponential mean-square stability and a prescribed disturbance attenuation level of the resulting filter error system. A novel approach is employed in showing the robust exponential mean-square stability. The exponential decay rate can be directly estimated using matrices of the Lyapunov-Krasovskii functional and its derivative. A delay-range-dependent condition in the form of LMIs is derived for the solvability of this H^∞ filtering problem, and the desired filter can be constructed with solutions of the LMIs. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Improved results on robust exponential stability criteria for neutral-type delayed neural networks

In this paper, we investigate the problem of robust global exponential stability analysis for a class of neutral-type neural networks. The interval time-varying delays allow for both slow and fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. Improved global exponential stability condition is derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed nominal and robust stability criteria is delay-dependent and characterized by linear-matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.     

Switching signal design for global exponential stability of uncertain switched nonlinear systems with time-varying delay

The switching signal (switching law) design for robust global exponential stability of switched nonlinear systems is investigated in this paper. LMI-based delay-dependent criteria are proposed to design the switching signal and guarantee the global exponential stability. Free weighting matrix and additional nonnegative inequality approaches are used in this paper to find the less conservative stability results. Finally, some numerical examples are illustrated to show the main improvement.     

Sampled-data control of uncertain switched neutral nonlinear systems under asynchronous switching

The robust exponential stabilization for a class of the uncertain switched neutral nonlinear systems with time-varying delays based on the sampled-data control is investigated in this paper. The closed-loop system with sampled-data control is modeled as a continuous time system with a time-varying piecewise continuous control input delay. Considering the relationship between the sampling period and the dwell time of two switching instants, sampling interval with no switching and sampling interval with one switching are discussed, respectively. By Wirtinger-based inequality, Wirtinger-based double integral inequality, and free-weighting matrix technique, some delay-dependent sufficient conditions are given to guarantee the exponential stability of uncertain switched neutral nonlinear systems under asynchronous switching. In addition, sampled-data controllers can also be designed by special operations of matrices. Finally, two numerical examples are used to show the effectiveness of the approach proposed in this paper.     

时变时滞BAM神经网络系统的指数稳定性分析

利用Lyapunov稳定性理论和线性矩阵不等式技术,得到了保证时变时滞BAM神经网络系统指数稳定性的时滞依赖稳定性准则.所给的准则可用Matlab中的LMI控制工具箱进行验证.仿真实例进一步说明了结果的有效性.     

Delay-range-dependent exponential stability criteria and decay estimation for switched Hopfield neural networks of neutral type

This paper is concerned with the problem of delay-range-dependent global exponential stability and decay estimation for a class of switched Hopfield neural networks (SHNNs) of neutral type. An average dwell time method is introduced into switched Hopfield neural networks. By constructing a new Lyapunov–Krasovskii functional and designing a switching law, some criteria are proposed for guaranteeing exponential stability for a given system, while the exponential decay estimation is explicitly developed for the states. A numerical example is provided to demonstrate the effectiveness of the main results.     

带有变化分布时滞的复值神经网络Lagrange稳定性

研究了带有变化分布时滞的复值神经网络Lagrange稳定性问题.通过构造合适的Lyapunov Krasovskii泛函, 并使用矩阵不等式技巧,建立了网络全局指数Lagrange稳定性的判定条件.提供的判据是复值线性矩阵不等式, 能够使用MATLAB软件的YALMIP工具箱快速计算.     

Neural networks with discrete and distributed time-varying delays: A general stability analysis

In this paper, the global asymptotic and exponential stability are investigated for a class of neural networks with both the discrete and distributed time-varying delays. By using appropriate Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique, several delay-dependent sufficient conditions are obtained to guarantee the global asymptotic and exponential stability of the addressed neural networks. These conditions are expressed in terms of LMIs, and are dependent on both the discrete and distributed time delays. Therefore, the stability of the neural networks can be checked readily by resorting to the Matlab LMI toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the differentiability of the discrete and distributed time-varying delays, which means that our results generalize and further improve those in the earlier publications. A simulation example is given to show the effectiveness and less conservatism of the obtained conditions.     

Robust L2–L∞ filtering for switched systems under asynchronous switching

This paper investigates the problem of robust L₂–L_∞ filtering for continuous-time switched systems under asynchronous switching. When there exists asynchronous switching between the filter and the system, based on the average dwell time approach, sufficient conditions for the existence of a linear filter that guarantee the filtering error system to be exponentially stable with a prescribed weighted L₂–L_∞ performance for switched systems are derived, and filter parameters can be obtained by solving a set of matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

New results on exponential passivity of neural networks with time-varying delays

The problem of delay-dependent exponential passivity analysis is investigated for neural networks with time-varying delays. By use of a linear matrix inequality (LMI) approach, a new exponential passivity criterion is proposed via the full use of the information of neuron activation functions and the involved time-varying delays. The obtained results have less conservativeness and less number of decision variables than the existing ones. A numerical example is given to demonstrate the effectiveness and the reduced conservatism of the derived results.     

Robust asymptotic stability for BAM neural networks with time-varying delays via LMI approach

Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.