On the improvement of linear discrete system stability: the maximal set of the \(F\)-admissible initial states
type: Item
instance of: scholarly article
title: On the improvement of linear discrete system stability: the maximal set of the \(F\)-admissible initial states
zbMATH Open document ID: 1066.93046
author: Mostafa Rachik
author: M. Lhous
author: Abdessamad Tridane
published in: Rocky Mountain Journal of Mathematics
publication date: 2005-03-11T00:00:00Z
review text: A discrete linear control system is considered under the assumption that its output is stabilizable by a given state-feedback control law. The author characterizes the set of all initial states \(x_0\) for which the output function \(y(i)\) of the closed-loop system satisfies the constraints \(\| y(i)\| \leq \alpha_i\), for all positive integer numbers \(i\). Here, the positive numbers \(\alpha_i\) are appropriately chosen and can be interpreted as ``a desired degree'' of stability. An algorithm for constructing this set of initial states is proposed and some numerical simulations are presented. The case of discrete-time delayed control systems is also studied.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 2144271
zbMATH Keywords: linear systems
zbMATH Keywords: feedback-stability
zbMATH Keywords: transients
zbMATH Keywords: region of stabilization
zbMATH Keywords: discrete system
zbMATH Keywords: linear control system
zbMATH Keywords: degree of stability
reviewed by: Mikhail Krastanov
Wikidata QID: Q56786977
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069845
OpenAlex ID: W2052674790
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DOI: 10.1216/RMJM/1181069845
description: scientific article; zbMATH DE number 2144271