论文标题
讨论有限和固定时间收敛算法的最新结果的三个示例
Discussion of Three Examples to Recent Results of Finite- and Fixed-Time Convergent Algorithms
论文作者
论文摘要
本说明讨论了最近的技术通信论文[1]中给出的三个示例，其中解决了[2,3,4]中介绍的结果。结果表明，第一个示例（[1]，第3节）与[2]的结果无关。第二个示例（[1]，第4节）建立了一个众所周知的事实，即连续差异化器才能完全区分信号，只有当其第二个导数相等的零时。本说明提供了一种将[3]中介绍的算法扩展到一般情况的方法。最后，第三个示例（[1]，第5节）提出了与[4]的定理1相关的特定案例。但是，在选择控制收益的最实际情况下，[4]的定理1仍然有效。 [4]中定理2的结果也估计固定收敛时间。
This note discusses three examples given in the recent technical correspondence paper [1], which addresses the results presented in [2,3,4]. It is shown that the first example ([1], Section 3) is irrelevant to the results of [2]. The second example ([1], Section 4) establishes a well-known fact that a continuous differentiator can exactly differentiate a signal, only if its second derivative is equal zero. This note provides a method to extend the algorithms presented in [3] to the general case. Finally, the third example ([1], Section 5) presents a particular case related to Theorem 1 of [4]. Theorem 1 of [4] remains, however, valid in the most practical case of selecting control gains. The result of Theorem 2 in [4] estimating the fixed convergence time holds as well.
