具有非线性扰动的变时滞中立型系统鲁棒稳定性新判据

研究一类具有非线性扰动的时变时滞中立型系统鲁棒稳定性问题。基于直接Lyapunov Krasovskii泛函并结合自由权矩阵方法的分析方法,建立了线性矩阵不等式(LMI)形式的离散时滞和中立时滞均相关稳定性判据。与以往方法不同,在处理泛函导数时,该方法不包含任何模型变换和涉及交叉项的处理,只是通过引入相关项自由权矩阵,充分考虑各项之间的相互关系,降低了结论的保守性。最后,利用Matlab的LMI工具箱进行了的数值仿真, 算例仿真表明所提出的判据的有效性。     

多参数线性时滞系统的稳定性准则

针对带有多参数扰动的线性时滞系统,利用二次型加积分项的Ｌｙａｐｕｎｏｖ泛函,导出了系统鲁棒稳定的时滞无关准则。由于准则给出的扰动界关于参数空间的原点可以是非对称的,充分利用了不确定性的结构特点,因此在很大程度上扩大了稳定参数城。     

一类具有扇区非线性的时变时滞系统的绝对稳定性

讨论一类具有扇区非线性的时变时滞系统的绝对稳定性问题.基于时滞分段的思想,构造一种新的Lyapunov 泛函,进一步应用自由权矩阵结合积分不等式方法,并充分考虑时变时滞和时滞上界之间的关系,得到了基于LMI的具有更低保守性的时滞相关绝对稳定条件.最后,数值实例表明所提方法的有效性和相比已有结果的优越性.     

鲁棒镇定受到干扰的非线性微分包含系统

研究带有干扰的非线性微分包含系统的镇定问题. 基于凸锥Lyapunov函数方法, 首先, 对于无干扰的这类系统, 设计可使闭环系统全局镇定的连续反馈控制律. 其次, 通过状态反馈, 对于受到两类有界干扰的这类微分包含系统的可达集进行了估计. 最后, 通过一个仿真例子说明所提出的设计方法的有效性.     

关于非线性时滞系统的鲁棒稳定性条件的讨论

1　引　言在《自动化学报》1 999年第 6期中 ,短文“非线性时滞系统的稳定性分析及鲁棒稳定性分析”[1 ] 用 Lyapunov函数方法分别讨论了确定性和不确定性非线性时滞系统的稳定性 .对于确定性系统得到了一种基于 LMI的渐近稳定充分条件 ,并研究了不确定性系统的鲁棒稳定性问题 .但由于该文对 Razumikhin定理的理解有误 ,有关鲁棒稳定性的结论 (定理 1、推论 1 )是不正确的 .对于 Razumikhin定理 ,文 [2 ]给出了一种所谓的改进型 Razumikhin定理 .但有人提出质疑 ,问题在于没有正确理解 Razumikhin定理 [3,4] .文 [1 ]虽然没有直接提到 R…     

多时滞奇异系统鲁棒稳定性分析

讨论了多时滞奇异系统的鲁棒稳定性问题．通过构造一种新的Lyapunov—Krasovskii泛函（LKF）,结合离散化LKF理论,给出了多时滞奇异系统正则、脉冲自由和渐近稳定的充分条件,并将该结论推广到含有范数有界不确定性的多时滞奇异系统．数值算例验证了该方法的有效性和可行性．     

一类参数不确定非线性系统的鲁棒稳定性

本文分析了一类参数不确定非线性系统，给出了其鲁棒稳定性的若干判据，为寻找非线性系统的参数鲁棒空间提供了一种途径，最后通过简单数据算例说明了本文结论的有效性。     

非线性时滞系统的稳定性分析及鲁棒稳定性条件

研究非线性时滞系统的稳定性.应用Lyapunov函数,分别讨论确定性和不确定性非线性时滞系统.对于确定性系统,给出其零解渐近稳定的充分条件;对于不确定性系统,给出其零解鲁棒稳定的充分条件.最后通过两个实例说明所给方法的有效性.     

一类不确定系统的鲁棒绝对稳定性

本文考虑一类不确定系统的绝对稳定性问题,系统的线性部分乃顶点模型的凸组合,非线性部分是一个非线性扇区如通常绝对稳定性问题中那样。我们将给出一个类似的圆判据,它说,所有顶点或边系统的某些频域条件可保证整个不确定系统是绝对稳定的。由于边系统仅含单参数,这样就大大地降低了原问题的计算复杂性。     

一类非线性广义系统的时滞相关耗散控制

针对一类带有非线性摄动的广义时滞系统,研究了时滞相关的鲁棒耗散问题.讨论了此类非线性广义时滞系统的鲁棒耗散性.同时对此类非线性广义时滞系统的二次稳定性进行了研究,分别用线性矩阵不等式（LMI）的方法给出了充分条件,也给出了时滞相关的鲁棒耗散的时滞上界.并且,给出了时滞相关的鲁棒耗散的状态反馈控制器.最后,通过例子验证了定理的可行性.     

Stability analysis of time-delay systems via free-matrix-based double integral inequality

Based on the free-weighting matrix and integral-inequality methods, a free-matrix-based double integral inequality is proposed in this paper, which includes the Wirtinger-based double integral inequality as a special case. By introducing some free matrices into the inequality, more freedom can be provided in bounding the quadratic double integral. The connection of the new integral inequality and Wirtinger-based double one is well described, which gives a sufficient condition for the application of the new inequality to be less conservative. Furthermore, to investigate the effectiveness of the proposed inequality, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. Numerical examples are given to demonstrate the advantages of the proposed method.     

Delay-range-dependent stability criterion for interval time-delay systems with nonlinear perturbations

In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii (LK) functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality (LMI) framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.     

Exponential stability analysis of time-delay systems based on Taylor expansion-based weighted integral inequality

This paper investigates the problem of exponential stability analysis of linear time-delay systems. First, based on the Gram-Schmidt-based integral inequality and the Taylor expansion of exponential function, we develop a new weighted multiple integral inequality called Taylor expansion-based weighted integral inequality. Second, a new Lyapunov-krasovskii functional is constructed, and then, with the help of the Taylor expansion-based inequality, a new exponential stability criterion is established in terms of linear matrix inequality. Finally, numerical examples are presented to show the effectiveness of the newly established stability criterion.     

Globally asymptotic stabilization for nonlinear time-delay systems with ISS inverse dynamics

The output feedback stabilization is considered for a class of nonlinear time-delay systems with inverse dynamics in this paper.An appropriate state observer is constructed for the unmeasurable system states in order to realize the control objective.By adopting the backstepping and Lyapunov-Krasovskii functional methods,a systematic design procedure for a memoryless output feedback control law is presented.It is shown that the designed controller can make the closed-loop system globally asymptotically stable while keeping all signals bounded.An illustrative example is discussed to show the effectiveness of the proposed control strategy.     

具有时变时滞的递归神经网络的渐近稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间.研究了带时变时滞的递归神经网络的全局渐近稳定性.首先将要研究的模型转化为描述系统模型,然后利用Lyapunov-Krasovskii稳定性定理、线性矩阵不等式(LMI)技术、S过程和代数不等式方法,得到了确保时变时滞递归神经网络渐近稳定性的新的充分条件,并将它应用于常时滞神经网络和时滞细胞神经网络模型,分别得到了相应的全局渐近稳定性条件.理论分析和数值模拟显示,所得结果为时滞递归神经网络提供了新的稳定性判定准则.     

Stability of diffusion stochastic functional differential equations with Markov parameters

The paper justifies the second Lyapunov method for diffusion stochastic functional differential equations with Markov parameters, which generalize stochastic diffusion equations without aftereffect. Analogs of Lyapunov stability theorems, which generalize the results for systems with finite aftereffect, are proved. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 74–88, January–February 2008.     

时滞系统稳定性分析:一种积分等式方法

提出一种积分等式方法研究时滞系统稳定性问题.该方法是已有积分不等式方法的改进.结合自由权矩阵构建积分等式,且自由权矩阵的选取由Lyapunov-Krasovskii泛函的导数确定,从而在稳定条件的推导过程中,不引入任何模型转换及限界方法.基于该方法,可得到具有更低保守性的稳定条件.仿真例子说明了所提方法的有效性.     

带有非线性扰动的时变时滞系统的稳定性准则

研究了带有非线性扰动的时变时滞系统的稳定性问题.基于时滞分割方法,提出了保守性更小的系统稳定性分析准则.利用一个自由参数将时滞区间分割为2个子区间,进而构造了含有时滞分割点状态信息和3重积分项的Lyapunov-Krasovskii泛函,并采用自由矩阵积分不等式界定泛函导数中的交叉项.基于Lyapunov稳定性定理,得到了以线性矩阵不等式描述的时滞相关型稳定性准则.数值算例表明该稳定性准则能够得到更大的时滞上界,与已有结果相比具有更小的保守性.     

Lie-algebraic stability conditions for nonlinear switched systems and differential inclusions

We present a stability criterion for switched nonlinear systems which involves Lie brackets of the individual vector fields but does not require that these vector fields commute. A special case of the main result says that a switched system generated by a pair of globally asymptotically stable nonlinear vector fields whose third-order Lie brackets vanish is globally uniformly asymptotically stable under arbitrary switching. This generalizes a known fact for switched linear systems and provides a partial solution to the open problem posed in [D. Liberzon, Lie algebras and stability of switched nonlinear systems, in: V. Blondel, A. Megretski (Eds.), Unsolved Problems in Mathematical Systems and Control Theory, Princeton University Press, NJ, 2004, pp. 203–207.]. To prove the result, we consider an optimal control problem which consists in finding the “most unstable” trajectory for an associated control system, and show that there exists an optimal solution which is bang-bang with a bound on the total number of switches. This property is obtained as a special case of a reachability result by bang-bang controls which is of independent interest. By construction, our criterion also automatically applies to the corresponding relaxed differential inclusion.