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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 (2): 183-195.doi: 10.3969/j.issn.1005-3085.2022.02.002

• • 上一篇    下一篇

异步切换下切换系统的动态输出反馈保成本控制

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:2022-04-15 发布日期:2022-06-15
  • 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).

Dynamic Output Feedback Guaranteed Cost Control of Switched 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:2022-04-15 Published:2022-06-15
  • 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：

作为一类重要的混杂系统，切换系统由若干个子系统以及一个协调各子系统之间切换的切换信号构成，在自然科学、工程控制和社会系统等方面有着广泛的应用。在对切换系统的控制问题进行研究时，一般假设子系统和控制器同步运行。然而，在实际工程控制中，控制器的切换相对于子系统的切换存在切换时延，从而产生异步切换。因此，对异步切换下的切换系统研究是十分必要的。针对一类异步切换下切换系统的动态输出反馈保成本控制问题进行了研究。报告了切换系统的研究现状以及异步切换下切换系统的最新研究成果。利用分段李雅普诺夫函数法和平均驻留时间法，得到了使得异步切换下的闭环切换系统稳定的动态输出反馈控制器存在的充分条件。从线性矩阵不等式的角度，提出了异步切换动态输出反馈保成本控制器设计方案，并给出成本上界的优化方法。最后，通过一个数值算例说明了提出的方法的有效性。

关键词: 切换系统, 保成本控制, 动态输出反馈, 平均驻留时间, 异步切换, 线性矩阵不等式

Abstract:

As an important hybrid system, switching system is composed of several subsystems and a switching signal to coordinate the switching between subsystems. It is widely used in natural science, engineering control and social systems. For the control problem of switched systems, it is generally assumed that the subsystem and controller operate synchronously. However, in practical engineering control, the switching of the controllers experiences a time delay with respect to that of subsystems, which results in the asynchronous switching. It is very necessary to study the switching system under asynchronous switching. The problem of dynamic output feedback guaranteed cost control for a class of switched systems under asynchronous switching is studied. The research status of switched systems and the latest research results of switched systems under asynchronous switching are reported. By using the piecewise Lyapunov function approach and the average dwell time technique, a sufficient condition for the existence of dynamic output feedback controllers is derived, which guarantees the exponential stability of the closed-loop system. Dynamic output feedback guaranteed cost controllers for switched systems under asynchronous switching are designed in terms of linear matrix inequalities. Moreover, an upper bound of the guaranteed cost function is obtained. The optimization problem to minimize the guaranteed cost is solved. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Key words: switched systems, guaranteed cost control, dynamic output feedback, average dwell time, asynchronous switching, linear matrix inequality

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