网络化非周期采样控制系统的主动时间滞后控制:随机脉冲切换系统方法  

Active Time⁃Delay Control of Networked Control Systems With Aperiodic Sampling:a Stochastic Impulsive Switched System Approach

作　　者：贺彦君 马伟伟 池小波[3] HE Yanjun;MA Weiwei;CHI Xiaobo(School of Statistics,Shanxi University of Finance and Economics,Taiyuan 030006,P.R.China;School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006,P.R.China;School of Mathematical Sciences,Shanxi University,Taiyuan 030006,P.R.China)

机构地区：[1]山西财经大学统计学院,太原030006 [2]山西财经大学应用数学学院,太原030006 [3]山西大学数学科学学院,太原030006

出　　处：《应用数学和力学》2021年第4期422-430,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(61803244);山西省应用基础研究计划青年科技研究基金(201901D211416);山西省高等学校科技创新项目(2019L0488)。

摘　　要：研究了一类带有随机丢包的非周期采样网络化控制系统的镇定问题.不同于传统观点往往将时滞看作系统稳定性的消极因素,考虑时间滞后对系统稳定性的积极影响,并提出一个新颖的主动时间滞后控制方法来镇定该系统.为了分析时间滞后控制的积极作用并获得较低保守性的结论,首先把带随机丢包的非周期采样系统建模为带固定切换率的随机脉冲切换系统,并在均方意义下提出一个新的分离引理用于分析随机脉冲切换系统的稳定性.然后,基于环⁃泛函方法和所提的分离引理,以线性矩阵不等式形式给出随机脉冲切换系统的均方稳定性判据.进一步,利用区间分割技术得到改进的均方稳定性判据.最后,利用一个经典的数值例子来验证所得稳定判据的有效性和所提方法的优势.The stabilization problem for a class of networked control systems with aperiodic sampling and sto⁃chastic packet dropouts was studied.Other than the traditional view that a time delay was often a negative factor of system stability,the positive effect was considered and a novel active time⁃delay control method was pro⁃posed to stabilize the systems.To analyze the positive effects of the time delay control and to obtain some less conservative conclusions,the aperiodic sampled⁃data system with stochastic packet dropouts was firstly mod⁃eled as a stochastic impulsive switched system with a fixed switching law.Then a new separation lemma was presented in a mean square sense to analyze the stability of the stochastic impulsive switched system.Based on the loop⁃functional method and the proposed separation lemma,the mean square stability criterion for the sto⁃chastic impulsive switched system was obtained in terms of linear matrix inequalities.Furthermore,the refined mean square stability criterion was given with an interval segmentation technique.Finally,a classical numerical example illustrates the validity of the obtained stability criteria and the advantages of the proposed method.

关 键 词：网络控制系统 非周期采样 脉冲切换系统 随机数据丢包 时间滞后控制 

分 类 号：O231.3[理学—运筹学与控制论]