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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

• • 上一篇    下一篇

非线性扰动的切换系统的异步控制：模态依赖的平均驻留时间方法

高  娟1,   李同彬2   

  1. 1. 哈尔滨师范大学数学科学学院，哈尔滨 150001；2. 哈尔滨师范大学经济学院，哈尔滨 150001
  • 出版日期:2022-12-15 发布日期:2022-12-15
  • 通讯作者: 李同彬 E-mail: litongbin006@163.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).

Asynchronous Control of Switched Systems with Nonlinear Perturbation: a Mode-dependent Average Dwell Time Approach

GAO Juan1,   LI Tongbin2   

  1. 1. School of Mathematical Sciences, Harbin Normal University, Harbin 150001;
    2. School of Economics, Harbin Normal University, Harbin 150001
  • Online:2022-12-15 Published:2022-12-15
  • Contact: T. Li. E-mail address: litongbin006@163.com
  • Supported by:
    The Basic Scientific Research Project of Provincial Colleges and Universities in Heilongjiang Province (2017-KYYWF-0142).

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摘要：

研究了一类具有非线性扰动的切换系统的异步控制问题，异步是指控制器的切换相对于子系统的切换经历时间延迟。利用异步切换系统状态方程的解析解直接研究系统动力学，无需构造任何李雅普诺夫函数。提出了保证闭环系统在模态依赖平均驻留时间(MDADT)方案下指数稳定的充分条件。MDADT意味着每个子系统都有自己的平均驻留时间(ADT)，这比ADT更具一般性。此外，利用线性矩阵不等式方法设计了异步切换控制器。最后，通过数值算例说明了该方法的有效性。

关键词: 切换系统, 异步控制, 非线性扰动, 模型依赖平均驻留时间, 线性矩阵不等式

Abstract:

This paper studies the asynchronous control problem for a class of switched systems with nonlinear perturbation. Asynchrony means that the switching of the controllers experien-ces a time delay with respect to that of the subsystems. The analytical solution to the state equation of the asynchronously switched systems is utilized to study the dynamics of systems directly without constructing any Lyapunov function. Sufficient conditions that ensure the exponential stability of the closed-loop system under the mode-dependent average dwell time (MDADT) scheme are proposed. MDADT means that each subsystem has its own average dwell time (ADT), which is more general than ADT. Moreover, asynchronously switched controllers are designed in terms of a set of solvable linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

Key words: switched system, asynchronous control, nonlinear perturbation, mode-dependent average dwell time, linear matrix inequalities

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