离散切换正时滞系统在异步切换下的镇定性  

Stabilization of Discrete Switched Positive Time-delay Systems Under Asynchronous Switching

作　　者：刘婷婷 吴保卫[2] 刘丽丽[2] 王月娥[2] LIU TINGTING;WU BAOWEI;LIU LILI;WANG YUE-E(School of Science,Xi'an Polytechnic University,Xi'an 710048,China;College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710119,China)

机构地区：[1]西安工程大学理学院,西安710048 [2]陕西师范大学数学与信息科学学院,西安710119

出　　处：《应用数学学报》2018年第6期721-734,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(61403241);西安工程大学博士科研启动金(BS1619);陕西省教育厅(17JK0340);河南省科技厅基础与前沿计划(162300410076);河南省教育厅高等学校重点科研(16A110020)资助项目

摘　　要：本文主要讨论含有时变时滞的离散切换正系统的异步镇定性.首先,通过构造适当的Lyapunov-Krasovskii泛函,得到离散切换正时滞系统在模型依赖平均驻留时间(MDADT)切换信号下指数稳定的一个充分条件.其次,通过允许所构造的Lyapunov-Krasovskii泛函在被激活的子系统和控制器不匹配的时间区间内递增,基于MDADT切换信号,得到存在一类状态反馈控制器使得闭环系统在异步切换下是正的且是指数稳定的一些充分条件.最后,给出两个数值例子说明所提出方法的有效性.The asynchronous stabilization of discrete switched positive systems(DSPSs)with time-varying delays is discussed in this paper. Firstly, by constructing an appropriate Lyapunov-Krasovskii functional, a sufficient condition is derived for the exponential stability of discrete switched positive time-delay systems under the switching signal with modedependent average dwell time(MDADT). Secondly, by allowing the Lyapunov-Krasovskii functional to increase during the mismatched period between the activated subsystems and the controllers, with the aid of MDADT switching signal, some sufficient conditions are obtained for the existence of state feedback controllers such that the resulting closed-loop system is positive and exponentially stable under asynchronous switching. Finally, two numerical examples are given to illustrate the validity of the proposed methods.

关 键 词：切换正系统 模型依赖平均驻留时间 异步切换 时变时滞 

分 类 号：O231[理学—运筹学与控制论]