Improved stability analysis on delayed neural networks with linear fractional uncertainties

The paper is concerned with robust stability for generalized neural networks (GNNs) with both interval time-varying delay and time-varying distributed delay. Through partitioning the time-delay, choosing one augmented Lyapunov-Krasovskii functional, employing free-weighting matrix method and convex combination, the sufficient conditions are obtained to guarantee the robust stability of the concerned systems. These stability criteria are presented in terms of linear matrix inequalities (LMIs) and can be easily checked. Finally, three numerical examples are given to demonstrate the effectiveness and reduced conservatism of the obtained results.     

Robust exponential stability and stabilizability of linear parameter dependent systems with delays

The robust exponential stability and stabilizability problems are addressed in this paper for a class of linear parameter dependent systems with interval time-varying and constant delays. In this paper, restrictions on the derivative of the time-varying delay is not required which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive delay-dependent exponential stability and stabilizability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to illustrate the effectiveness of our theoretical results.     

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters

This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequality (LMI) by constructing new Lyapunov-Krasovskii functionals via generalized eigenvalue problems (GEVPs). The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Robust synchronization of impulsively-coupled complex switched networks with parametric uncertainties and time-varying delays

This paper presents a general impulsively-coupled complex switched network (ICCSN) model with parametric uncertainties and multiple Time-varying Delays in both the linear and nonlinear terms. The model is more general than those in the literature in that it contains switching behaviors on nodes and impulsive effects in the whole topology. Robust synchronization of ICCSNs with parametric uncertainties and time-varying delays is investigated. Based on the Lyapunov stability theory, delay-independent synchronization conditions for ICCSNs with uncertainties and delays are obtained. In addition, we consider five special synchronization cases: ICCSNs with delays in both the linear and nonlinear terms, ICCSNs with parametric uncertainties and delays either in the linear or in the nonlinear term, ICCSNs without switching behaviors but with parametric uncertainties and delays, and impulsively-switched-coupled complex switched network with uncertainties and delays. A systematic-design procedure is presented, and a numerical example is carried out to demonstrate the effectiveness of the proposed synchronization strategy. A comparative study of the maximum impulsive intervals for synchronization is presented for all special cases.     

Synchronization stability of general complex dynamical networks with time-varying delays: A piecewise analysis method

The synchronization problem of some general complex dynamical networks with time-varying delays is investigated. Both time-varying delays in the network couplings and time-varying delays in the dynamical nodes are considered. The delays considered in this paper are assumed to vary in an interval, where the lower and upper bounds are known. Based on a piecewise analysis method, the variation interval of the time delay is firstly divided into several subintervals, by checking the variation of the derivative of a Lyapunov function in every subinterval, then the convexity of matrix function method and the free weighting matrix method are fully used in this paper. Some new delay-dependent synchronization stability criteria are derived in the form of linear matrix inequalities. Two numerical examples show that our method can lead to much less conservative results than those in the existing references.     

A novel approach on stabilization for linear systems with time-varying input delay

This paper presents new results on delay-dependent stability and stabilization for linear systems with interval time-varying delays. Some less conservative delay-dependent criteria for determining the stability of the time-delay systems are obtained in this paper. Based on the stability conditions, we propose a new state transformation technology to facilitate controller designing efficiently and computationally. The method is also applicable to the existing stability conditions reported by now, while the existing technologies may fail to derive computational control procedures from the stability conditions. Finally, some numerical examples well illustrate the effectiveness of the proposed method.     

Delay-dependent stability of neutral systems with time-varying delays using delay-decomposition approach

This paper is concerned with the problem of asymptotic stability of neutral systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality to ensure a large upper bound of the time-delay by non-uniformly dividing the delay interval into multiple segments. A new Lyapunov-Krasovskii functional is constructed with different weighting matrices corresponding to different segments in the Lyapunov-Krasovskii functional, where both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

不确定变时滞系统的一个时滞相关稳定性判据

本文讨论不确定变时滞系统的稳定性问题.基于一个新的Lyapunov泛函,并利用一种新的方法处理不确定项,得到了不确定变时滞系统的一个时滞相关的稳定性判据,并利用矩阵不等式的形式给出该判据.与已有文献相比较,所得结论允许时滞导数(?)(t)(?)1且具有较少的限制条件,因此具有较弱的保守性.最后,通过两个例子验证了所给结论的正确性.     

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.     

State estimation of neural networks with both time-varying delays and norm-bounded parameter uncertainties via a delay decomposition approach

This paper is concerned with the state estimation problem for neural networks with both time-varying delays and norm-bounded parameter uncertainties. By employing a delay decomposition approach and a convex combination technique, we obtain less conservative delay-dependent stability criteria to guarantee the existence of desired state estimator for the delayed neural networks. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed approach.     

Improved stability criteria for neutral type Lur’e systems with time-varying delays

In this letter, the problem of stability analysis for neutral type Lur’e systems with interval time-varying delays is considered. By introducing a novel Lyapunov–Krasovskii (L–K) functional and utilizing second order reciprocal convex combination technique and Finsler lemma, an improved delay-dependent stability criteria is derived in terms of linear matrix inequalities (LMIs). The information about the time-varying delays and their upper bounds are fully used in the L–K functional. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.     

Stability analysis of Cohen–Grossberg neural network with both time-varying and continuously distributed delays

In this paper, the Cohen–Grossberg neural network model with both time-varying and continuously distributed delays is considered. Without assuming both global Lipschitz conditions on these activation functions and the differentiability on these time-varying delays, applying the idea of vector Lyapunov function, M-matrix theory and inequality technique, several new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of equilibrium point for Cohen–Grossberg neural network with both time-varying and continuously distributed delays. These results generalize and improve the earlier publications. Two numerical examples are given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of the Cohen–Grossberg neural networks.     

A new augmented Lyapunov-Krasovskii functional approach for stability of linear systems with time-varying delays

This paper proposes improved delay-dependent conditions for asymptotic stability of linear systems with time-varying delays. The proposed method employs a suitable Lyapunov-Krasovskii’s functional for new augmented system. Based on Lyapunov method, delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Three numerical examples are included to show that the proposed method is effective and can provide less conservative results.     

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.     

Stochastic Stability Analysis for Switched Genetic Regulatory Networks with Interval Time-Varying Delays Based on Average Dwell Time Approach

In this article, the problem of stochastic stability analysis for switched stochastic genetic regulatory networks with interval time-varying delays based on average dwell time approach is investigated. By constructing the piecewise Lyapunov-Krasovskii functional, delay-dependent stability conditions are derived by using free-weighting matrix and convex combination approach. The derived stability conditions are expressed in terms of linear matrix inequalities which can be easily solved by using the MATLAB LMI control toolbox. Finally, numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed theoretical results.     

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.     

PERIODIC SOLUTIONS AND STABILITY ANALYSIS FOR NEURAL NETWORKS WITH TIME-VARYING DELAY

1 IntroductionIt is well known that both in biological and man-made neural systems, inte-gl.ation afld communication delays are ubiquitous, and often become sources ofinstabilitY' The de1ays in electronic neural networks are usually time varying,and sometimes vary vio1ently with time due to the finite switching speed ofamplifiers and faults in the electrical circuit. They s1ow down the transmissionrate and tend to introduce some degree of instability in circuits. Therefore,fast response must …     

Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

In this paper, the problem of robust exponential stability is investigated for a class of stochastically nonlinear jump systems with mixed time delays. By applying the Lyapunov–Krasovskii functional and stochastic analysis theory as well as matrix inequality technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. Time delays proposed in this paper comprise both time-varying and distributed delays. Moreover, the derivatives of time-varying delays are not necessarily less than 1. The results obtained in this paper extend and improve those given in the literature. Finally, two numerical examples and their simulations are provided to show the effectiveness of the obtained results.     

分布时滞系统的动态输出反馈鲁棒稳定

主要研究了一类具分布时变时滞不确定系统的输出反馈鲁棒稳定问题.基于动态输出反馈和Lyapunov-Krasovskii泛函,给出了闭环系统与时滞相关的鲁棒稳定的条件.所得条件为线性矩阵不等式形式,便于运用内点算法进行求解.     

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper is concerned with the problem of stability of neutral systems with interval time-varying delays and nonlinear perturbations. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.