含非线性扰动的变时滞中立系统时滞相关稳定性新条件

研究一类含非线性扰动和混合时变时滞的中立型系统时滞相关鲁棒稳定性问题.通过构造包含三重积分项的Lyapunov-Krasovskii的泛函,结合积分不等式和自由权矩阵技术,建立了基于线性矩阵不等式(LMI)形式的离散时滞和中立时滞均相关的稳定性新判据.判据扩大了系统稳定所允许的最大时滞上界范围,具有更低的保守性.利用MATLAB的LMI工具箱进行了数值仿真,仿真算例验证了所提出的稳定性判据的有效性.     

Numerical detection of instability regions for delay models with delay-dependent parameters

In this paper we are interested in gaining local stability insights about the interior equilibria of delay models arising in biomathematics. The models share the property that the corresponding characteristic equations involve delay-dependent coefficients. The presence of such dependence requires the use of suitable criteria which usually makes the analytical work harder so that numerical techniques must be used. Most existing methods for studying stability switching of equilibria fail when applied to such a class of delay models. To this aim, an efficient criterion for stability switches was recently introduced in [E. Beretta, Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal. 33 (2002) 1144–1165] and extended [E. Beretta, Y. Tang, Extension of a geometric stability switch criterion, Funkcial Ekvac 46(3) (2003) 337–361]. We describe how to numerically detect the instability regions of positive equilibria by using such a criterion, considering both discrete and distributed delay models.     

Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term,discrete and unbounded distributed delays

In this article, a class of bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with time delay in the leakage term, discrete and unbounded distributed delays is formulated to study the global asymptotic stability. This approach is based on the Lyapunov–Krasovskii functional with free-weighting matrices. Using linear matrix inequality (LMI), a new set of stability criteria for BAM FCNNs with time delay in the leakage term, discrete and unbounded distributed delays is obtained. Also, the stability behavior of BAM FCNNs is very sensitive to the time delay in the leakage term. In the absence of a leakage term, a new stability criteria is also derived by employing a Lyapunov–Krasovskii functional and using the LMI approach. Our results establish a new set of stability criteria for BAM FCNNs with discrete and unbounded distributed delays. Numerical examples are provided to illustrate the effectiveness of the developed techniques.     

Some new simple stability criteria of linear neutral systems with a single delay

This article mainly considers the linear neutral delay-differential systems with a single delay. Using the characteristic equation of the system, new simple delay-independent asymptotic and exponential stability criteria are derived in terms of the matrix measure, the spectral norm and the spectral radius of the corresponding matrices. Numerical examples demonstrate that our criteria are less conservative than those of previous corresponding results [L.M. Li, Stability of linear neutral delay-differential systems, Bull. Aust. Math. Soc. 38 (1988) 339–344; G.D. Hu, G.D. Hu. Some simple criteria for stability of neutral delay-differential systems, Appl. Math. Comput. 80 (1996) 257–271; D.Q. Cao, Ping He, Sufficient conditions for stability of linear neutral systems with a single delay, Appl. Math. Lett. 17 (2004) 139–144; G.D. Hu, G.D. Hu, B. Cahlon, Algebraic criteria for stability of linear neutral systems with a single delay, J. Comput. Appl. Math. 135 (2001) 125–130].     

Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay

In this paper, we consider the problem of robust stability of a class of linear uncertain neutral systems with interval time-varying delay under (i) nonlinear perturbations in state, and (ii) time-varying parametric uncertainties using Lyapunov-Krasovskii approach. By constructing a candidate Lyapunov-Krasovskii (LK) functional, that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMI) to compute the maximum allowable bound for the delay-range within which the uncertain neutral system under consideration remains asymptotically stable. The reduction in conservatism of the proposed stability criterion over recently reported results is attributed to the fact that time-derivative of the LK functional is bounded tightly without neglecting any useful terms using a minimal number of slack matrix variables. The analysis, subsequently, yields a stability condition in convex LMI framework, that can be solved non-conservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.     

Improved stability and H∞ performance for neutral systems with uncertain Markovian jump

This paper addresses the problem of the delay-dependent stability and $H\infty$ performance for neutral systems with uncertain Markovian jump; the uncertainty of Markovian jump refers to the partial information on transition probability. In order to highlight the methods for the analysis of the systems, the neutral delay is assumed same as discrete delay. By the novel constructed Lyapunov functional, combining with the delay decomposition technique and free matrices, and using the new inequality rather than the Jensen inequality, the delay-dependent stability conditions are firstly obtained for the two kinds of neutral dynamical systems. Based on the stability condition, the $H\infty$ performance result for the systems with Markovian jump is secondly provided. All of the delay-dependent stabilization results are formulated in terms of LMIs, which can be easily checked by the LMI control toolbox in Matlab. Finally, two numerical examples are given to show the validity and potential of the developed criteria.     

随机时滞控制系统的均方BIBO稳定性

本文研究了具有时滞和非线性扰动的随机控制系统的均方有界输入-有界输出(BIBO)稳定.首先,探讨了具有离散时滞和非线性扰动的随机系统的均方BIBO稳定性问题,在此基础上,进一步研究带有离散时滞和分布时滞以及非线性扰动的随机系统的均方BIBO稳定性.通过设计合理的控制器,建立合适的Lyapunov泛函,结合Riccati矩阵方程,得到时滞依赖的均方BIBO稳定性条件.     

Delay-dividing approach for absolute stability of Lurie control system with mixed delays

This paper studies the absolute stability problem for a Lurie control system with nonlinearity located in an infinite sector and finite one. By dividing the discrete delay interval into multiple segments and choosing proper Lyapunov functionals, some delay dependent stability criteria are derived to guarantee the stability of the Lurie control system. It is established theoretically that the criteria are less conservative than the previous ones. Numerical examples demonstrate the validity of the proposed criteria.     

New delay-dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties

This paper investigates the robust stability of uncertain neutral system with time-varying delay and nonlinear uncertainties. By using Lyapunov method and linear matrix inequality technology, a new delay-dependent stability criteria is obtained and formulated in terms of linear matrix inequalities (LMIs) which can be easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.     

线性中立型单延迟系统李代数稳定性判据

研究了线性中立型单延迟微分系统的稳定性.从矩阵李代数可解性角度,推导出新的简单的延迟独立稳定性判据.该新判据的重要意义和优越性在于首次突破了以往大多数相关文献的稳定性判据在应用上受条件‖C‖<1,ρ(|C|)<1或ρ(|N|)<1的限制,从而首次成功确定了在‖C‖≥,ρ(|C|)≥1和ρ(|N|)≥1的情形下中立型延迟微分系统渐近稳定性.最后,通过两个例子显示了新判据的优越性.     

Delay-dependent and delay-independent stability criteria for a delay differential system

For a linear delay differential system with two coefficients and one delay, we establish some necessary and sufficient conditions on the asymptotic stability of the zero solution, which are composed of delay-dependent and delay-independent stability criteria. On the former criterion, the range of the delay is explicitly given.

     

SYNCHRONIZATION OF SINGULAR MARKOVIAN JUMPING NEUTRAL COMPLEX DYNAMICAL NETWORKS WITH TIME-VARYING DELAYS VIA PINNING CONTROL

This article discusses the synchronization problem of singular neutral complex dynamical networks(SNCDN) with distributed delay and Markovian jump parameters via pinning control. Pinning control strategies are designed to make the singular neutral complex networks synchronized. Some delay-dependent synchronization criteria are derived in the form of linear matrix inequalities based on a modified Lyapunov-Krasovskii functional approach. By applying the Lyapunov stability theory, Jensen's inequality, Schur complement,and linear matrix inequality technique, some new delay-dependent conditions are derived to guarantee the stability of the system. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.     

Improved delay-dependent stability criterion for neural networks with time-varying delay

In this paper, the problem of delay-dependent asymptotic stability criterion for neural networks with time-varying delay has been considered. A new class of Lyapunov functional which contains a triple-integral term is constructed to derive some new delay-dependent stability criteria. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

网络化非周期采样控制系统的主动时间滞后控制: 随机脉冲切换系统方法

研究了一类带有随机丢包的非周期采样网络化控制系统的镇定问题.不同于传统观点往往将时滞看作系统稳定性的消极因素,考虑时间滞后对系统稳定性的积极影响, 并提出一个新颖的主动时间滞后控制方法来镇定该系统.为了分析时间滞后控制的积极作用并获得较低保守性的结论,首先把带随机丢包的非周期采样系统建模为带固定切换率的随机脉冲切换系统, 并在均方意义下提出一个新的分离引理用于分析随机脉冲切换系统的稳定性.然后,基于环 泛函方法和所提的分离引理,以线性矩阵不等式形式给出随机脉冲切换系统的均方稳定性判据.进一步,利用区间分割技术得到改进的均方稳定性判据.最后,利用一个经典的数值例子来验证所得稳定判据的有效性和所提方法的优势.     

Modeling the role of constant and time varying recycling delay on an ecological food chain

We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the daily variation in nutrient recycling and deduce the stability criteria of the variable delay model. A comparison of the variable delay model with the constant delay one is performed to unearth the biological relevance of oscillating delay in some real world ecological situations. Numerical simulations are done in support of analytical results.     

Improved delay-dependent stability criteria for continuous system with two additive time-varying delay components

This paper investigated the problem of improved delay-dependent stability criteria for continuous system with two additive time-varying delay components. Free weighting matrices and convex combination method are not involved, which achieves much less numbers of linear matrix inequalities (LMIs) and LMIs scalar decision variables. By taking advantage of integral inequality and new Lyapunov–Krasovskii functional, new less conservative delay-dependent stability criterion is derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

New results for global stability of a class of neutral-type neural systems with time delays

This paper studies the global convergence properties of a class of neutral-type neural networks with discrete time delays. This class of neutral systems includes Cohen–Grossberg neural networks, Hopfield neural networks and cellular neural networks. Based on the Lyapunov stability theorems, some delay independent sufficient conditions for the global asymptotic stability of the equilibrium point for this class of neutral-type systems are derived. It is shown that the results presented in this paper for neutral-type delayed neural networks are the generalization of a recently reported stability result. A numerical example is also given to demonstrate the applicability of our proposed stability criteria.     

A graph‐theoretic approach to stability of neutral stochastic coupled oscillators network with time‐varying delayed coupling

In this paper, a graph‐theoretic approach for checking exponential stability of the system described by neutral stochastic coupled oscillators network with time‐varying delayed coupling is obtained. Based on graph theory and Lyapunov stability theory, delay‐dependent criteria are deduced to ensure moment exponential stability and almost sure exponential stability of the addressed system, respectively. These criteria can show how coupling topology, time delays, and stochastic perturbations affect exponential stability of such oscillators network. This method may also be applied to other neutral stochastic coupled systems with time delays. Finally, numerical simulations are presented to show the effectiveness of theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.