不确定时变时滞切换中立系统的非脆弱H∞滤波器设计
Non-Fragile H∞ Filter Design for Uncertain Switched Neutral Systems with Time-Varying Delays
摘要: 本文研究了一类带有时变状态时滞和时变中立时滞的参数不确定切换系统的控制问题，并对其问题设计了具有H∞性能指标的非脆弱滤波器。讨论的参数不确定性是范数有界的，滤波器是带有中立时滞的非脆弱H∞滤波器。目的是对于所容许的不确定性和时变时滞，设计一个非脆弱H∞滤波器，得到使闭环系统切换镇定并满足给定的H∞性能指标γ的充分条件。首先，利用Lyapunov稳定性理论，构造了合适的Lyapunov泛函，利用时滞导数的上界对不等式进行放缩，得到具有H∞性能指标的线性矩阵不等式。利用凸组合方法和线性矩阵不等式，构造了对应的切换规则。其次，利用线性矩阵不等式的方法设计了非脆弱H∞滤波器，得到的滤波器存在充分条件。最后，通过数值仿真证明了所提结果的有效性和可行性。本文提出的线性矩阵不等式具有决策变量少、参数多的特点，可以最大程度地降低结果的保守性。
Abstract: In this paper, we investigated the control problem of a class of parameter uncertain switched systems with time-varying state and neutral delay, and designed non-fragile filters with H∞ performance index for these problems. The parameter uncertainties discussed are norm-bounded, and the H∞ filters are non-fragile with neutral delays. To design a non-fragile H∞ filter for the admissible uncertainties and time-varying delays, we obtained sufficient conditions for the closed-loop system to switch calming and satisfy the given H∞ performance index γ. Firstly, a suitable Lyapunov function is constructed by using Lyapunov stability theory, and the inequality is deflated using the upper bound of the time delay derivative, and we obtained a linear matrix inequality with H∞ performance index. Using convex combination methods and linear matrix inequalities, the corresponding switching rules are constructed. Second, the non-fragile H∞ filter is designed by using the method of linear matrix inequality, and the obtained filter has sufficient conditions. Finally, the validity and feasibility of the theoretical results are demonstrated by numerical simulations. The linear matrix inequality proposed in the paper has the feature of few decision variables with many parameters, which can minimize the conservative of the results.
文章引用：亚库甫·卡斯木, 姑丽加玛丽·麦麦提艾力. 不确定时变时滞切换中立系统的非脆弱H∞滤波器设计[J]. 动力系统与控制, 2024, 13(2): 54-67. https://doi.org/10.12677/dsc.2024.132006

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