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一类不确定时滞系统的鲁棒稳定性 总被引:2,自引:0,他引:2
给出了不确定时滞系统鲁棒稳定的若干结果,同时讨论了这类系统的稳定度,改进了前人关于时滞系统稳定性和鲁棒稳定性的一些结论,并给出了应用的例子。 相似文献
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对于一类不确定状态时变时滞系统,利用基于时滞划分的Lyapunov-Krasovskii泛函讨论其稳定性,并得到以LMI形式给出的一种保守性小的稳定性条件,最后通过分析并给出了保证系统鲁棒稳定的H∞控制器,数值实例表明了方法的有效性. 相似文献
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在社会经济系统中,广泛地存在着多重时滞的正系统.对于连续型时滞正系统的全时滞稳定问题,文献[1]已给出简单而实用的代数判别方法.本文通过对离散型多重时滞正系统的深入研究,给出一个全时滞稳定的简单代数充要判别方法,并建立了时滞系统渐近稳定与时滞系统全时滞稳定之间的等价关系,避免了在稳定性判别中由于大量状态扩展所带来的困难.此外本文还建立了稳定性与正平衡点之间的等价关系,并讨论了系数 相似文献
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研究了变时滞退化Lurie控制系统的绝对稳定性问题.基于Lyapunov稳定性理论,利用线性矩阵不等式方法给出了系统绝对稳定的判别准则.讨论了变时滞退化Lurie直接控制系统和间接控制系统的绝对稳定性,得到绝对稳定性的充分条件仅依赖于时滞导数的大小,且时滞可以是无界函数:最后给出了实例说明本文结果的有效性. 相似文献
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研究了脉冲信号作用下随机时滞系统的指数稳定性问题,基于Razumikhin方法建立了判断随机时滞脉冲系统指数稳定性判定定理,并给出收敛速度的求法.作为应用,考查了典型随机时滞混沌系统的脉冲同步问题,得到脉冲信号作用下随机时滞混沌系统的收敛速度.数值模拟结果验证了理论结果的正确性. 相似文献
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《数学的实践与认识》2013,(9)
研究了一类具有混合时滞和非线性干扰中立型不确定随机神经网络鲁棒稳定性,所考虑的不确定为范数有界,混合时滞由离散和分布时滞组成,借助李雅普诺夫函数和随机稳定性理论,利用伊藤公式,给出并证明了使系统鲁棒稳定的充分条件,所有结果以线性矩阵不等式的形式给出,数值算例表明了所给方法的有效性. 相似文献
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Yu Zhang 《Mathematical Methods in the Applied Sciences》2012,35(11):1287-1299
The purpose of this paper is to investigate the robust exponential stability of discrete‐time uncertain impulsive neural networks with time‐varying delay. By using Lyapunov functions together with Razumikhin technique, some new robust exponential stability criteria are presented. The obtained results show that the robust stability can be retained under certain impulsive perturbations for the neural network, which has the robust stability property. The obtained results also show that impulses can robustly stabilize the neural network, which does not have the robust stability property. Some examples, together with their simulations, are also given to show the effectiveness and the advantage of the presented results. It should be noted that the impulsive robust exponential stabilization result for discrete‐time neural network with time‐varying delay is given for the first time. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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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. 相似文献
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Yang Li Zhang Qingling Liu Guoyi 《Annals of Differential Equations》2005,21(3):497-502
We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stability are given by the linear matrix inequalities (LMIs), then the time-delay bound and the delay dependent robust dissipative state feedback controller are presented. 相似文献
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In this paper, we consider the problem of delay-dependent robust stability of a class of uncertain discrete-time systems with time-varying delay using Lyapunov functional approach. Two categories of time-varying uncertainties are considered for the robust stability analysis: viz., (i) nonlinear perturbations and (ii) norm-bounded uncertainties. In the proposed stability analysis, by exploiting a candidate Lyapunov functional, and using minimal number of slack matrix variables, less conservative stability criteria are developed in terms of linear matrix inequalities (LMIs) for computing the maximum allowable bound of the delay-range, within which, the uncertain system under consideration remains asymptotically stable in the sense of Lyapunov. The effectiveness of the proposed stability criteria is demonstrated using standard numerical examples. 相似文献
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Toshiyuki Koto 《Frontiers of Mathematics in China》2009,4(1):113-129
Stability properties of implicit-explicit (IMEX) linear multistep methods for ordinary and delay differential equations are
analyzed on the basis of stability regions defined by using scalar test equations. The analysis is closely related to the
stability analysis of the standard linear multistep methods for delay differential equations. A new second-order IMEX method
which has approximately the same stability region as that of the IMEX Euler method, the simplest IMEX method of order 1, is
proposed. Some numerical results are also presented which show superiority of the new method.
相似文献
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讨论了一般时间尺度上时滞脉冲系统的双测度稳定性问题.我们引进了一个新的概念即一般时间尺度上时滞脉冲系统的(h_0,h)稳定性.利用Lyapunov函数法和分析法得到了一般时间尺度上时滞脉冲系统解的双测度稳定性判据.最后给出了一个例子以说明本文结论的有效性. 相似文献
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不确定时滞Lurie系统的鲁棒绝对稳定性分析 总被引:1,自引:0,他引:1
研究了一类不确定Lurie时滞系统的鲁棒绝对稳定性问题,不确定项范数有界。通过构造特殊的李亚普诺夫函数,分别考虑了时滞相关和时滞无关两情况,得到了系统鲁棒绝对稳定的充分条件。 相似文献
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This paper investigates the problem of robust reliable control for a class of switched nonlinear systems with time delay and actuator failures under asynchronous switching. When the switching instants of the controller experience delays with respect to those of the system, a kind of reliable controller design method is proposed, and the dwell time approach is utilized for the stability analysis. Sufficient conditions for the existence of the reliable controller are formulated in terms of a set of LMIs. Then the proposed approach is extended to take into account switched delay systems with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. 相似文献
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The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and unbounded delay is addressed. On the assumption that the interconnected functions of the studied systems satisfy the Lipschitz condition, by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems under arbitrary switching are obtained. The proposed method, which neither require the individual subsystems to share a Common Lyapunov Function (CLF), nor need to involve the values of individual Lyapunov functions at each switching time, provide a new way of thinking to study the stability of arbitrary switching. In addition, the proposed criteria are explicit, and it is convenient for practical applications. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the proposed theories. 相似文献