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Discussion of Three Examples to Recent Results of Finite- and Fixed-Time Convergent Algorithms

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Document pages: 6 pages

Abstract: This note discusses three examples given in the recent technicalcorrespondence paper [1], which addresses the results presented in [2,3,4]. Itis shown that the first example ([1], Section 3) is irrelevant to the resultsof [2]. The second example ([1], Section 4) establishes a well-known fact thata continuous differentiator can exactly differentiate a signal, only if itssecond derivative is equal zero. This note provides a method to extend thealgorithms 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 ofselecting control gains. The result of Theorem 2 in [4] estimating the fixedconvergence time holds as well.

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