Finite time stability and stabilization of a class of continuous systems
Finite time stability and stabilization of a class of continuous systems
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DOI：
10.1016/j.jmaa.2005.11.046
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发表时间：
2006-11
影响因子：
1.3
通讯作者：
Emmanuel Moulay;W. Perruquetti
中科院分区：
文献类型：
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作者：
Emmanuel Moulay;W. Perruquetti
研究了在向前时间内满足解的唯一性的连续系统xstec =f（x）的有限时间稳定性.利用李雅普诺夫函数给出了这类系统有限时间稳定的充分必要条件。然后，给出了一类CLk-仿射系统xstec =f（x）+g（x）u的有限时间镇定的充要条件，其中闭环系统的稳定时间函数为CL 0类.最后，利用控制李雅普诺夫函数证明了一个不等式，给出了显式反馈控制。
Finite time stability is investigated for continuous system x˙=f(x) which satisfies uniqueness of solutions in forward time. A necessary and sufficient condition for finite time stability is given for this class of systems using Lyapunov functions. Then, a necessary and sufficient condition is developed for finite time stabilization of class CLk-affine systems x˙=f(x)+g(x)u involving a class CL0-settling-time function for the closed-loop system. Finally an explicit feedback control is addressed by using a control Lyapunov function verifying a certain inequality.