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]

Document Type : Brief Note

Author

Department of Electrical Engineering, Sahand University of Technology, P.O. Box: 51335-1996, Sahand New Town, Tabriz, Iran

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.

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