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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (4): 571-588.doi: 10.3969/j.issn.1005-3085.2022.04.006

• • 上一篇    下一篇

异步切换下切换时变时滞系统的保成本控制

李同彬1,   高  娟2   

  1. 1. 哈尔滨师范大学经济学院，哈尔滨 150001;
    2. 哈尔滨师范大学数学科学学院，哈尔滨 150001
  • 出版日期:2022-08-15 发布日期:2022-10-15
  • 通讯作者: 高 娟 E-mail: gaojuan006@126.com
  • 基金资助:
    黑龙江省省属高等学校基本科研业务费科研项目 (2017-KYYWF-0142).

Guaranteed Cost Control of Switched Time-varying Delay Systems under Asynchronous Switching

LI Tongbin1,   GAO Juan2   

  1. 1. School of Economics, Harbin Normal University, Harbin 150001;
    2. School of Mathematical Sciences, Harbin Normal University, Harbin 150001
  • Online:2022-08-15 Published:2022-10-15
  • Contact: J. Gao. E-mail address: gaojuan006@126.com
  • Supported by:
    The Basic Scientific Research Business Cost Scientific Research Project of Provincial Colleges and Universities in Heilongjiang Province (2017-KYYWF-0142).

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摘要：

切换系统是一种重要的混杂系统，由若干子系统及决定子系统之间切换的切换信号组成。在工程应用中，控制器切换与子系统的切换会存在时延，即异步切换。研究了异步切换下的时变时滞系统的保成本控制问题，利用分段李雅普诺夫函数法和平均驻留时间法，得到保成本控制器存在的充分条件，并从线性矩阵不等式的角度，设计了一个异步切换保成本控制器，使得系统具有鲁棒性能。最后，给出了一个数值例子验证提出的方法的有效性。

关键词: 时变时滞, 保成本控制, 平均驻留时间, 异步切换, 线性矩阵不等式

Abstract:

Switched system is an important hybrid system, which is composed of several subsystems and switching signals that determine the switching between subsystems. In engineering applications, there inevitably exists asynchronous switching between the system mode and the controller, i.e., asynchronous switching. The problem of guaranteed cost control of switched time-varying delay systems is investigated under asynchronous switching. A sufficient condition for the existence of the GCC law is derived by using the piecewise Lyapunov function approach and the average dwell time technique, which guarantees the exponential stability and a certain upper bound for the cost function of the closed-loop system. Then, the design problem of the GCC law is solved in terms of linear matrix inequalities, an asynchronous switching GCC controller is designed to make the system robust. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Key words: time-varying delay, guaranteed cost control, average dwell time, asynchronous switching, linear matrix inequality

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