异步切换下一类带有时变时滞非线性切换系统的指数镇定  

Exponential Stabilization for a Class of Nonlinear Switched Systems with Time-Varying Delay Under Asynchronous Switching

作　　者：王永昭[1] 李天瑞 刘倩 WANG Yong-zhao;LI Tian-rui;LIU Qian(School of Mathematics and Statistics,Anyang Normal University,Anyang 455000,China;School of Science,Nanjing University of Science and Technology,Nanjing 210094,China;School of Civil Engineering and Architecture,Anyang University,Anyang 455000,China)

机构地区：[1]安阳师范学院数学与统计学院,河南安阳455000 [2]南京理工大学理学院,江苏南京210094 [3]安阳学院建筑工程学院,河南安阳455000

出　　处：《数学的实践与认识》2018年第24期279-287,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金青年科学基金(71502050);河南省高等学校重点科研项(18A630001,18A110010);安阳师范学院2017年度校级教学研究项目(ASJY-YB-047)资助

摘　　要：研究了在异步切换下一类带有时变时滞非线性切换系统指数镇定问题,其中控制器的切换时刻滞后于系统的切换时刻.构造了与参数相关的Lyapunov-Krasovskii函数,且在控制器与子系统不匹配区间内增加.利用矩阵不等式和平均驻留时间相结合的方法,建立了时变时滞非线性切换系统在异步切换下指数镇定的充分条件.另外,在异步切换下通过矩阵的特殊变形,最终设计出控制器.最后给出仿真算例验证了所得结果的有效性.The problem of exponential stabilization for a class of switched nonlinear systems with time-varying delay under asynchronous switching is investigated,where the switching instants of the controller experience delays with respect to those of the system.Parameterdependent Lyapunov-Krasovskii functional are constructed,which are allowed to increase during the running time of active subsystems with the mismatched controller.Using the method of combining matrix inequality and average dwell time,a sufficient condition for exponential stabilization of switched nonlinear systems with time-varying delay under asynchronous switching is established.In addition,through the special deformation of the matrix,the controller of the switching system are designed under asynchronous switching.Finally,the simulation example illustrate the effectiveness of the theoretical results.

关 键 词：异步切换 时变时滞 非线性切换系统 平均驻留时间 LYAPUNOV-KRASOVSKII函数 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]