| 引用本文: | 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.[点击复制] |
| CHEN Zhi-hua,XIE Yong-chun.Finite time stability analysis of the linear time-varying systems[J].Control Theory and Technology,2018,35(4):485~496.[点击复制] |
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| 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 |
| 摘要点击 5327 全文点击 2399 投稿时间：2017-06-14 修订日期：2017-12-09 |
| 查看全文 查看/发表评论 下载PDF阅读器 |
| DOI编号 10.7641/CTA.2017.70407 |
| 2018,35(4):485-496 |
| 中文关键词 线性时变系统 一致 有限时间稳定 收缩稳定 调节时间 包线 |
| 英文关键词 linear time-varying system uniform finite time stability contractive stability settling time envelope |
| 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. |
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| 中文摘要 |
| 针对一般非线性时变系统的有限时间稳定性分析问题, 考虑到系统初始时刻在有限时间区间内的变化, 本
文分别提出了一般非线性时变系统的一致有限时间稳定性,一致收缩稳定性和固定调节时间一致收缩稳定性定义.
针对一类线性时变系统, 基于计算系统的所有轨线的包线的思想, 本文分别给出了判定该类系统的收缩稳定性、固
定调节时间收缩稳定性、一致有限时间稳定性、一致收缩稳定性、固定调节时间一致收缩稳定性的充分必要条件,
同时给出了判定该类系统一致收缩稳定性及固定调节时间一致收缩稳定性的3个充分条件. 进一步, 本文将所得定
理结果推广到了周期线性时变系统, 所得结论为判定周期线性时变系统关于任意初始时刻的一致有限时间稳定性,
一致收缩稳定性及固定调节时间一致收缩稳定性提供了理论依据. 最后, 以4个数值算例和两航天器相对运动过程
为例验证了本文结果的正确性. |
| 英文摘要 |
| 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. |
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