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1.
In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying
delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by
using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical
examples are given to illustrate the applicability of the results using standard numerical software. 相似文献
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一类基于观测器的非线性网络化控制系统的绝对稳定性 总被引:1,自引:0,他引:1
主要考虑了基于观测器的Lurie网络化控制系统的绝对稳定性问题. 由于采用了基于观测器的反馈控制器, 传感器到控制器的网络诱导时延和控制器到执行器的网络诱导时延不再能合并到一起处理. 首先通过状态增广方法将Lurie网络化控制系统建模为一个多时滞的Lurie系统, 然后利用Newton-Leibniz公式和添加自由权矩阵的方法给出了时滞依赖的稳定性条件. 在此基础上, 给出三种求解控制器和观测器增益矩阵的方法. 此外, 还分别给出了被控对象存在范数有界不确定性和结构不确定性时系统的鲁棒稳定性条件及鲁棒控制器设计方法, 所有得到的结果都是以线性矩阵不等式的形式给出的. 便于利用线性矩阵不等式工具包进行求解. 最后, 通过两个仿真算例说明了方法的可行性和有效性. 相似文献
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时变时滞Lurie控制系统的绝对稳定性 总被引:1,自引:0,他引:1
基于Lyapunov稳定性定理,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.讨论了具有多个时变时滞的Lurie直接控制系统和Lurie间接控制系统的绝对稳定性.所得结论是时滞无关的,即绝对稳定性充分条件仅依赖于时滞导数的大小,特别地,时滞可为无界函数.通过一个示例说明有时得到时滞相关的绝对稳定性条件比时滞无关的稳定性条件具有更大的保守性,促使今后寻找另外的方法和工具得到保守性较低的稳定性条件.仿真示例同时说明此方法对时滞为无界函数时的有效性. 相似文献
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具有时变时滞的Lurie系统绝对稳定性的时滞相关条件 总被引:3,自引:1,他引:2
Some delay-dependent absolute stability criteria for Lurie control systems with time-varying delay are derived, in which some free-weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. These criteria are based on linear matrix inequality(LMI) such that the upper bound of time-delay guaranteeing the absolute stability and the free-weighting matrices can be obtained through the solutions of the LMI. Moreover, the Lyapunov functional constructed by the solutions of these LMIs is adopted to guarantee the absolute stability of the systems. Finally, some examples are provided to demonstrate the effectiveness of the proposed methods. 相似文献
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Delay-dependent Conditions for Absolute Stability of Lurie Control Systems with Time-varying Delay 总被引:1,自引:0,他引:1
HE Yong WU Min 《自动化学报》2005,(3)
Some delay-dependent absolute stability criteria for Lurie control systems with time- varying delay are derived,in which some free-weighting matrices are used to express the relation- ships between the terms in the Leibniz-Newton formula.These criteria are based on linear matrix inequality(LMI) such that the upper bound of time-delay guaranteeing the absolute stability and the free-weighting matrices can be obtained through the solutions of the LMI.Moreover,the Lyapunov functional constructed by the solutions of these LMIs is adopted to guarantee the absolute stability of the systems.Finally,some examples are provided to demonstrate the effectiveness of the proposed methods. 相似文献
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New Augmented Lyapunov‐Krasovskii Functional for Stability Analysis of Systems with Additive Time‐Varying Delays
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This paper is concerned with stability analysis for continuous‐time systems with additive time‐varying delays in the Lyapunov‐Krasovskii(L‐K) framework. Firstly, in view of the relationships between the upper bounds of the two time‐varying delays, a new augmented L‐K functional is constructed by using the information of the two upper bounds. Secondly, the free‐matrix‐based integral inequality is used to estimate the derivative of the constructed L‐K functional. Thirdly, a less conservative criterion is derived to assess stability. Finally, a numerical example is presented to demonstrate the effectiveness of the criterion. 相似文献
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时变时滞Lurie非线性系统绝对稳定新判据 总被引:1,自引:0,他引:1
针对时变时滞Lurie非线性系统,应用增广Lyapunov-Krasovskii泛函结合自由权矩阵方法,研究其时滞相关绝对稳定性问题.通过保留Lyapunov-Krasovskii泛函导数中常被忽略的有用信息,充分考虑时变时滞、时滞上界及它们的差三者之间的关系,得到了具有更低保守性的基于线性矩阵不等式的时滞相关绝对稳定条件.数值实例表明,该方法得出的结果优于已有文献的结果. 相似文献
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用“二次型加积分项”形式的Lyapunov函数研究一类时变非线性控制系统的绝对稳定性,给出了系统绝对稳定的充分条件以及时变系数导数界限的估计,明显地优于[1]中的结果。 相似文献
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时变滞后Lurie型系统的改进稳定性准则 总被引:1,自引:0,他引:1
In this technical note, we present a new stability analysis procedure for ascertaining the delay-dependent stability of a class of Lurie systems with time-varying delay and sector-bounded nonlinearity using Lyapunov-Krasovskii (LK) functional approach. The proposed analysis, owing to the candidate LK functional and tighter bounding of its time-derivative, yields less conservative absolute and robust stability criteria for nominal and uncertain systems respectively. The effectiveness of the proposed criteria over some of the recently reported results is demonstrated using a numerical example. 相似文献
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基于LMI的非线性摄动系统鲁棒绝对稳定性判据 总被引:1,自引:0,他引:1
讨论了前馈通道同时存在对象和控制器的范数摄动,而反馈通道存在扇区非线性的摄动系统的稳定性问题.基于H∞理论和LMI方法,得到了一组由线性矩阵不等式表达的充分性条件,建立了判断非线性摄动系统鲁棒绝对稳定性的新判据. 相似文献
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本文利用Lyapunov泛函,对多变量的Lurie泛函型方程的控制系统给出了绝对稳定性的充分条件,把对一个变量的某些结果推广到了多变量。 相似文献
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研究了不确定Lurie时滞系统的绝对稳定问题。通过构造适当的Lyapunov泛函、引入一些自由权矩阵和充分考虑时滞导数的上限信息,得到了基于LMIs(线性矩阵不等式)形式的时滞相关绝对稳定性新准则,两个数值例子验证了所得结论的有效性和更弱保守性。 相似文献
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考虑具有时变时滞的Takagi-Sugeno模糊系统稳定性分析的问题.基于Lyapunov 稳定性理论,定义一个新的Lyapunov-Krasovskii泛函,使用恰当的界定技术处理Lyapunov-Krasovskii泛函求导过程中产生的积分项,以线性矩阵不等式的形式给出一个决策变量少、运算效率高、保守性小的时滞相关稳定性准则;此外,在理论推导过程中避免了一些现有文献理论推导过程中出现的问题.最后通过给出的数例验证了该稳定性准则的有效性. 相似文献
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针对一类含有不确定项的时变时滞动力系统,根据李雅普诺夫第二方法,采用线性矩阵不等式(LIM)处理方法,对其指数稳定问题进行了研究。通过构造适当的李雅普诺夫函数,利用积分不等式技术,得到一个不确定时滞相关系统指数稳定的新判据,并将其转化为线性矩阵不等式的形式,从而可以很方便地利用Matlab工具箱求解得到一般动力系统指数稳定的时滞的相关最大上界,最后通过数值例子说明结果的可行性,其结果具有较小的保守性,而且在实际应用有重要意义。 相似文献
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一类具有非线性扰动的多重时滞不确定系统鲁棒预测控制 总被引:1,自引:0,他引:1
针对一类具有非线性扰动且同时存在多重状态和输入时滞的不确定系统, 提出 一种鲁棒预测控制器设计方法. 基于预测控制滚动优化原理, 运用Lyapunov稳定性 理论和线性矩阵不等式 (Linear matrix inequalities, LMIs)方法, 首先近似求解无限时域二次性能指标优化问题, 然后优化非 线性扰动项所应满足的最大上界, 定量地研究鲁棒预测控制在范数有界意义下的扰动抑制 问题, 并给出了鲁棒预测控制器存在的充分条件. 最后通过仿真验证了所提方法的有效性. 相似文献
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This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii (L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method. 相似文献
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This paper is concerned with the robust stability of time‐varying delay systems with structured uncertainties. Stability conditions are provided through a Lyapunov‐Krasovskii functional (LKF) method. The proposed method introduces a linear function of the time‐varying delay to construct the LKF. With this function, two‐dimensional partition is conducted on the integral domain in the derivative of LKF. Quadratic convex combination then is employed to present stability criteria in the form of linear matrix inequalities (LMIs). The method not only exploits the information of delay at different time instants, but also enables the handling of its derivative to reduce conservatism. Numerical examples are given to show the effectiveness of our method. 相似文献
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This paper is mainly concerned with the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic neural networks with interval time-varying delay. With an appropriate augmented Lyapunov–Krasovskii functional (LKF) formulated, the convex combination method is utilised to estimate the derivative of the LKF. Some new delay-dependent exponential stability criteria for such systems are obtained in terms of linear matrix inequalities, which involve fewer matrix variables and have less conservatism. Finally, two illustrative numerical examples are given to show the effectiveness of our obtained results. 相似文献