Discussion of Three Examples to Recent Results of Finite- and Fixed-Time Convergent Algorithms
Abstract
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.
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Cite
@article{arxiv.2003.12674,
title = {Discussion of Three Examples to Recent Results of Finite- and Fixed-Time Convergent Algorithms},
author = {Michael Basin and Pablo Rodriguez-Ramirez},
journal= {arXiv preprint arXiv:2003.12674},
year = {2020}
}