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离散区间系统的H ∞ 鲁棒控制 总被引:1,自引:1,他引:0
研究离散区间系统的鲁棒稳定性分析和鲁棒控制问题,首先基于Riccati方程方法讨论系统的鲁棒稳定性,得到了检验该类系统鲁棒稳定的新的充分条件,然后给出了离散区间系统鲁棒控制器存在的充分条件,并通过求解修正的代数Riccati方程,给出了该控制器的设计方法。 相似文献
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基于第2类Fornasini-Machesini模型,研究离散区间2-D系统鲁棒稳定的问题.引入区间不确定性,建立离散区间2-D系统数学模型,根据2-D系统渐近稳定的一种Lyapunov不等式判据和一个对称区间矩阵正定性引理,给出离散区间2-D系统鲁棒稳定的一个充分条件,并通过数值算例表明所给出的离散区间2-D系统鲁棒稳定的充分条件是有效的. 相似文献
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用Lyapunov函数研究了具有单调扇形限制的多非线性项的区间离散Lurie系统的鲁棒绝对稳定性, 给出了此类区间离散Lurie系统的鲁棒绝对稳定性的矩阵不等式形式的代数判据, 并与区间对称矩阵稳定性建立了联系. 相似文献
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秦岭 《自动化技术与应用》2008,27(1):10-11
本文主要研究了离散区间系统的稳定性问题,以线性矩阵不等式的形式给出了离散区间系统鲁棒稳定性的充分条件,最后通过仿真验证了该方法是行之有效的。 相似文献
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研究了动态离散区间系统的鲁棒稳定性问题,提出了系统二次稳定的充分与必要条件,以及相应的稳定裕度的计算方法,并推广到离散参数不确定系统.所有结论以线性矩阵不等式(LMI)的形式给出.利用功能强大的LMI工具,求解非常方便.所给实例表明,该方法用于确定动态离散区间系统的鲁棒稳定性及其稳定裕度,非常有效. 相似文献
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区间离散广义系统的鲁棒稳定性分析 总被引:1,自引:0,他引:1
讨论一类区间离散广义系统的鲁棒稳定性问题。在给出区间离散广义系统的等价描述之后,基于线性矩阵不等式,得到了问题的充要条件,数值例子说明了该方法的正确性。 相似文献
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针对一类带有扰动、输入约束和凸多面体不确定性的区间时滞离散非线性系统, 提出一种鲁棒模型预测控制方法. 一方面, 利用min-max 模型预测控制求解鲁棒模型预测控制器, 以研究鲁棒预测控制在范数有界意义下的扰动抑制问题; 另一方面, 充分利用时滞的上下界信息构造Lyapunov 函数以得到控制器存在的充分条件. 最后给出了闭环系统鲁棒稳定性证明. 相似文献
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离散区间动力系统稳定性的新判据 总被引:1,自引:1,他引:0
本文运用抠间分析的方法讨论了离散区间动力系统的稳定性,推广著名的Jury判据、 Kharitonov判据和Routh-Hurwitz判据到离散区间动力系统,得到了离散是动力系统稳定的充分条件。本文的结论可完全用计算机程序实现。 相似文献
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非线性两端边值问题是在非线性最优控制计算中遇到的主要困难, 通常将其转化为线性两端边值问题的迭代求解.因此, 很有必要发展求解线性时变非齐次方程的两端边值问题的精确、高效算法. 本文通过引入区段混合能的概念, 将问题转化为区段的混合能矩阵及向量的求解, 进一步给出了它们的保辛摄动算法. 该算法具有很强的并行性, 高效而精确. 本文还指出经典的 Riccati 变换方法是该方法的一个特例. 数值算例验证了本文方法的有效性. 相似文献
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New delay range–dependent stability criteria for interval time‐varying delay systems via Wirtinger‐based inequalities 下载免费PDF全文
Reza Mohajerpoor Lakshmanan Shanmugam Hamid Abdi Rajan Rakkiyappan Saeid Nahavandi Peng Shi 《国际强度与非线性控制杂志
》2018,28(2):661-677
》2018,28(2):661-677
Stability conditions for time‐delay systems using the Lyapunov‐based methodologies are generically expressed in terms of linear matrix inequalities. However, due to assuming restrictive conditions in deriving the linear matrix inequalities, the established stability conditions can be strictly conservative. This paper attempts to relax this problem for linear systems with interval time‐varying delays. A double‐integral inequality is derived inspired by Wirtinger‐based single‐integral inequality. Using the advanced integral inequalities, the reciprocally convex combination techniques and necessary slack variables, together with extracting a condition for the positive definiteness of the Lyapunov functional, novel stability criteria, have been established for the system. The effectiveness of the criteria is evaluated via 2 numerical examples. The results indicate that more complex stability criteria not only improve the stability region but also bring computational expenses. 相似文献
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Shu-Xiang Guo 《International journal of systems science》2018,49(7):1491-1506
Interval models are frequently used for dealing with uncertainties of control systems. However, it is well known that direct analysis and synthesis of a controlled dynamic system with interval matrix uncertainties may be a NP-hard problem. In this work, an efficient methodology for robustness analysis and robust control design of dynamic systems with interval matrix uncertainties is presented systematically, in which the uncertainties appearing in the controlled plant and controller realisation are taken into account simultaneously in an integrated framework. The fundamental problems, such as quadratic stability, guaranteed cost control and H∞ control of uncertain systems are taken as examples to show the methodology. Necessary and sufficient conditions for linear dynamic systems with interval matrices are derived by transforming all the interval matrices into some more tractable forms. The whole reasoning process is logical and rigorous, and NP-hard problem is successfully avoided. The presented formulations are within the framework of linear matrix inequality and can be implemented conveniently. In contrast to existing vertex-set methods, in which the vertices of interval matrices need to be constructed and checked, the presented methods are more efficient. Three numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method. 相似文献
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本文用向量Lyapunov函数方法讨论了高维区间动力大系统的渐近稳定性,得到了区间动力系统渐近稳定的若干充分条件。 相似文献
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本语文针对一般的滞后动态系统建立了广义指数稳定性的充分和必要条件,并由所建立的充要条件得出了系统过渡过程的时变指数衰减估计,作为所建结果的应用,基于矩阵工给出了一类滞后动态系统过渡过程的相应指数衰减估计,本文揭示了所建衰减估计可好于那些仅基于充分稳定性条件所得的估计。 相似文献
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Wei-Jie Mao Jian Chu 《Automatic Control, IEEE Transactions on》2003,48(6):1007-1012
This note presents necessary and sufficient conditions for the quadratic stability and stabilization of dynamic interval systems. The results are obtained in terms of linear matrix inequalities (LMIs) and extended to the quadratic stability and stabilization of linear systems with uncertain parameters. With the powerful LMI toolbox, it is very convenient to solve these problems. The illustrative examples show that this method is effective and less conservative to check the robust stability and to design the stabilizing controller for dynamic interval systems. 相似文献
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Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances 总被引:1,自引:0,他引:1
In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure. 相似文献