控制理论与应用2018，Vol.35Issue(4)：485-496,12.DOI:10.7641/CTA.2017.70407
线性时变系统有限时间稳定性分析
Finite time stability analysis of the linear time-varying systems
摘要
Abstract
Considering the problem of the finite time stability analysis of the general nonlinear time-varying system with its initial time varying in a finite interval of time, the paper proposes the concepts of uniform finite time stability, uniform contractive stability and uniform contractive stability with fixed settling time,respectively. For a class of linear time-varying(LTV)systems,by computing the envelope of all of its trajectories,the corresponding sufficient and necessary decision theorems for its contractive stability, contractive stability with fixed settling time, uniform finite time stability, uniform contractive stability and uniform contractive stability with fixed settling time are derived respectively. Moreover, three sufficient decision theorems for the uniform contractive stability and uniform contractive stability with fixed settling time of the LTV systems are also proposed.Further,the obtained theorems are generalized to the periodic LTV system,and the generalized results provide theoretical basis for deciding the uniform finite time stability,uniform contractive stability and uniform contractive stability with fixed settling time of the periodic LTV system with respect to arbitrary initial time. Finally,four numerical examples and an example about relative motion process of two spacecraft are given to verify the correctness of the obtained results.关键词
线性时变系统/一致/有限时间稳定/收缩稳定/调节时间/包线Key words
linear time-varying system/uniform/finite time stability/contractive stability/settling time/envelope分类
信息技术与安全科学引用本文复制引用
陈志华,解永春..线性时变系统有限时间稳定性分析[J].控制理论与应用,2018,35(4):485-496,12.基金项目
国家重点基础研究发展计划"973"项目(2013CB733100),国家自然科学基金重点项目(61333008)资助.Supported by the National Key Basic Research and Development Program"973"(2013CB733100)and the State Key Program of National Natural Science of China(61333008). （2013CB733100）
