Corrections to “On the global practical stabilization of discrete-time switched affine systems: application to switching power converters” [Scientia Iranica (2021) 28(3), 1621-1642] and [Scientia Iranica (2021) 28(3), 1606-1620]
Department of Electrical Engineering, Sahand University of Technology, P.O. Box: 51335-1996, Sahand New Town, Tabriz, Iran
10.24200/sci.2024.61264.7230
Abstract
This note corrects the proof of Theorem 1 in \cite{Hejri20202}, the statement and proof of Lemma 1, and a part of proofs in Theorems 1 and 2 of \cite{Hejri20201}. A step is incorrect in the proof of Theorem 1 of \cite{Hejri20202} when showing a positive constant $\gamma$ exists to satisfy item (b) of Lemma 1. The error lies at the definition of function $\phi(s)$ in (35) where the norm function $\|e(k)\|$ must be replaced by the distance function $\|e(k)\|_{\mathcal{E}(P)}=\inf_{y\in\mathcal{E}}\|e(k)-y\|$ denoting the distance from point $e(k)$ to the ellipsoid $\mathcal{E}(P)$. Therefore, using (32) in \cite{Hejri20202} and Lyapunov set asymptotic stability arguments \cite{Goebel2012}, we can only conclude that $\phi(\|e(k)\|_{\mathcal{E}(P)})\rightarrow0$ as $k\rightarrow\infty$, and the existence of a positive constant $\gamma$ is not proved.
Hejri, M. (2024). Corrections to “On the global practical stabilization of discrete-time switched affine systems: application to switching power converters” [Scientia Iranica (2021) 28(3), 1621-1642] and [Scientia Iranica (2021) 28(3), 1606-1620]. Scientia Iranica, (), -. doi: 10.24200/sci.2024.61264.7230
MLA
Mohammad Hejri. "Corrections to “On the global practical stabilization of discrete-time switched affine systems: application to switching power converters” [Scientia Iranica (2021) 28(3), 1621-1642] and [Scientia Iranica (2021) 28(3), 1606-1620]". Scientia Iranica, , , 2024, -. doi: 10.24200/sci.2024.61264.7230
HARVARD
Hejri, M. (2024). 'Corrections to “On the global practical stabilization of discrete-time switched affine systems: application to switching power converters” [Scientia Iranica (2021) 28(3), 1621-1642] and [Scientia Iranica (2021) 28(3), 1606-1620]', Scientia Iranica, (), pp. -. doi: 10.24200/sci.2024.61264.7230
VANCOUVER
Hejri, M. Corrections to “On the global practical stabilization of discrete-time switched affine systems: application to switching power converters” [Scientia Iranica (2021) 28(3), 1621-1642] and [Scientia Iranica (2021) 28(3), 1606-1620]. Scientia Iranica, 2024; (): -. doi: 10.24200/sci.2024.61264.7230