切换正线性系统在模型依赖平均驻留时间下的异步L_(1)控制  

Asynchronous L_(1) control of switched positive systems with mode-dependent average dwell time

作　　者：刘婷婷 路俊影 安夏伶 LIU Tingting;LU Junying;AN Xialing(School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《哈尔滨商业大学学报（自然科学版）》2024年第4期441-448,共8页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：陕西省科技厅自然科学基金项目(2021JQ-657)。

摘　　要：研究一类切换正线性系统在模型依赖平均驻留时间(MDADT)切换信号下的异步L_(1)控制问题.通过构造适当的李亚普诺夫(Lyapunov)函数,基于MDADT切换信号,讨论了一类切换正线性系统在异步切换下的指数稳定性,并进一步给出了其在异步切换下具有指数的L_(1)-增益性能γ的充分条件.基于已建立的稳定性定理和MDADT切换信号,设计了一类异步状态反馈控制器,使得闭环系统在异步切换下是正的并且具有指数的L_(1)-增益性能γ,给出了求解控制器的增益矩阵K_(i)的具体算法.此外,所得结论都是以代数矩阵不等式的形式给出的,可以利用Matlab中的LP工具箱进行求解.给出了一个数值算例验证了所得结论的有效性和可行性.The asynchronous L_(1) control problem for a class of switched positive linear systems under mode-dependent average dwell time(MDADT)switching signal was investigated in this paper.By constructing an appropriate Lyapunov function,based on MDADT switching signal,the exponential stability of switched positive linear systems under asynchronous switching was discussed.Moreover,a sufficient condition of the exponential stability with L_(1)-gain performance γ under asynchronous switching was also given.Based on the established stability theorem and MDADT switching signal,a class of state feedback controller was designed to make the closed-loop system under MDADT was positive and exponential stability with L_(1)-gain performanceγ,and the specific algorithm for solving the gain matrix K_(i) of the controller was given.Moreover,the conclusions were given in the form of algebraic matrix inequalities,which can be solved by using the LP toolbox in Matlab.A numerical example was given to demonstrate the effectiveness and feasibility of the obtained results.

关 键 词：切换正系统 模型依赖平均驻留时间 LYAPUNOV函数 异步切换 指数稳定 L 1-增益性能 

分 类 号：O231.1[理学—运筹学与控制论]