CorrespondenceComments on “Design of Controllers with Arbitrary Convergence Time” [Automatica 112 (2020) 108710]☆,☆☆
Section snippets
On technical correctness
We examine first the meaning of the basic concepts, given by Pal et al. (2020) for the underlying system As in Pal et al. (2020), is the state of system (1), stands for the initial time, represents the constant parameters of the system, and is a nonlinear function such that .
Definition 3 of arbitrary time stability and Definition 4 of free-will arbitrary time stability, introduced in Pal et al. (2020), rely on the fixed-time stability
On novelty
Comment Definition 3 coins the term “arbitrary time stability”, which is just a re-branding of the pre-existing concept of “prescribed-time stabilization” in Song et al. (2017). Definition 3 trivially extends the prescribed-time stabilization concept to an infinite horizon by requiring the state to remain zero after the prescribed time.
Comment Using the logarithmic transformation in (8) of Song et al. (2017), Theorem 1 of Pal et al. (2020) is a direct consequence of Corollary 1
References (6)
- et al.
Design of controllers with arbitrary convergence time
Automatica
(2020) - et al.
Authors’ Reply To: (CI 20-0229) Comments on Design of controllers with arbitrary convergence time [Automatica 108710]
Automatica
(2020) - et al.
Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time
Automatica
(2017)
Cited by (1)
- ☆
The authors of the commented-on paper stand by the assertions and contributions of their paper.
- ☆☆
The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Editor André L. Tits.