On the improvement of linear discrete system stability: The maximal set of the F-admissible initial states

M. Rachik; M. Lhous; A. Tridane

doi:10.1216/rmjm/1181069845

On the improvement of linear discrete system stability: The maximal set of the F-admissible initial states

M. Rachik, M. Lhous, A. Tridane

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The linear controlled discrete system is supposed to be output stabilizable, i.e., lim_i→+∞ y(i) = 0. To improve the stability of the system we propose in this paper a theoretical and algorithmic characterization of all the initial states x0 for which y(i) ∈ B(0, α_i), for all i ≥ 0, where B(0, α_i) is the ball of center 0 and radius α_i, the sequence (α_i)i is appropriately chosen “α_i)_i can be interpreted as a desired degree of stability.”h The case of discrete delayed systems is also considered.

Original language	English
Pages (from-to)	1103-1120
Number of pages	18
Journal	Rocky Mountain Journal of Mathematics
Volume	34
Issue number	3
DOIs	https://doi.org/10.1216/rmjm/1181069845
Publication status	Published - 2004
Externally published	Yes

Keywords

Delayed system
Discrete control systems
Maximal set
Stability

ASJC Scopus subject areas

General Mathematics

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10.1216/rmjm/1181069845

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abstract = "The linear controlled discrete system is supposed to be output stabilizable, i.e., limi→+∞ y(i) = 0. To improve the stability of the system we propose in this paper a theoretical and algorithmic characterization of all the initial states x0 for which y(i) ∈ B(0, αi), for all i ≥ 0, where B(0, αi) is the ball of center 0 and radius αi, the sequence (αi)i is appropriately chosen “αi)i can be interpreted as a desired degree of stability.”h The case of discrete delayed systems is also considered.",

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AB - The linear controlled discrete system is supposed to be output stabilizable, i.e., limi→+∞ y(i) = 0. To improve the stability of the system we propose in this paper a theoretical and algorithmic characterization of all the initial states x0 for which y(i) ∈ B(0, αi), for all i ≥ 0, where B(0, αi) is the ball of center 0 and radius αi, the sequence (αi)i is appropriately chosen “αi)i can be interpreted as a desired degree of stability.”h The case of discrete delayed systems is also considered.

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KW - Discrete control systems

KW - Maximal set

KW - Stability

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On the improvement of linear discrete system stability: The maximal set of the F-admissible initial states

Abstract

Keywords

ASJC Scopus subject areas

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