离散时间切换系统L2增益与驻留时间关系分析
大连交通大学, 自动化与电气工程学院, 辽宁大连 116028
| 摘 要： | 本文主要研究离散时间切换系统在驻留时间（DT）切换条件下l2增益控制器的设计问题。到目前为止，系统l2增益稳定性与驻留时间的定量关系是切换系统领域中尚未解决的问题之一。不同于以往的研究结果，本文首次提出一种新的驻留时间依赖Lyapunov函数（DTDLF）得到更低保守性稳定性判据。此Lyapunov函数的创新之处在于它的构建不再是传统两步控制器设计法，而是将控制器和切换规律这两个设计任务合并在一个框架中，其中求解线性矩阵不等式（LMIs）只涉及一个步骤。与两步设计方案相比，此方法大大简化了设计过程。采用驻留时间依赖Lyapunov函数和驻留时间切换策略，设计了一种驻留时间依赖（DTD）H∞控制器，使系统具有全局一致渐近稳定（GUAS）性质，保证了H∞的性能指标。最后，通过一个数值算例来验证所得结果的有效性，经过仿真实验证实了所提出的设计方法能够保证更短的驻留时间界和较小的误差结果。 |
| 关 键 词： | l2增益; 驻留时间依赖李雅普诺夫函数; H∞控制器; 离散时间; 切换系统 |
| DOI： | 10.57237/j.se.2023.03.002 |
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收稿日期: 2023-04-26
接受日期: 2023-05-23
在线出版日期: 2023-06-15
Analysis of the Relation Between L2 Gain and Dwell Time in Discrete Time Switching System
School of Electric Engineering and Automation, Dalian Jiaotong University, Dalian 116028, China
| Abstract: | This paper focuses on the design of l2 gain controller for discrete time switching systems with dwell time (DT) switching. So far, the quantitative relationship between l2 gain stability and dwell time is one of the unsolved problems in the field of switching systems. Different from previous studies, a novel dwell time dependent Lyapunov function (DTDLF) is proposed in this paper for the first time to obtain a less conservative stability criterion. The innovation of this Lyapunov function lies in that it is no longer built by the traditional two-step controller design method, but combines the two design tasks of controller and switching law into one framework, in which solving linear matrix inequalities (LMIs) involves only one step. Compared with the two-step design scheme, this method greatly simplifies the design process. Based on the resident time dependent Lyapunov function and the resident time switching strategy, a dwell time dependent (DTD) H∞ controller is designed such that the system is globally uniformly asymptotically stable (GUAS) and has a guaranteed H∞ performance index. Finally, a numerical example is given to verify the validity of the proposed design method. The simulation results show that the proposed design method can guarantee a shorter resident time limit and a smaller error result. |
| Keywords: | l2 Gain; New Dwell Time Dependent Lyapunov Function; H∞ Control; Discrete Time; Switching System |
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