Discrete Tagaki-Sugeno models for control: ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Discrete Tagaki-Sugeno models for control: Where are we?
Author(s) :
Guerra, Thierry-Marie [Auteur correspondant]
Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201 [LAMIH]
Kruszewski, Alexandre [Auteur]
Systèmes Non Linéaires et à Retards [SyNeR]
Lauber, Jimmy [Auteur]
Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201 [LAMIH]
Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201 [LAMIH]
Kruszewski, Alexandre [Auteur]

Systèmes Non Linéaires et à Retards [SyNeR]
Lauber, Jimmy [Auteur]
Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201 [LAMIH]
Journal title :
Annual Reviews in Control
Pages :
37-47
Publisher :
Elsevier
Publication date :
2009-04
ISSN :
1872-9088
English keyword(s) :
Discrete Takagi–Sugeno model
Non quadratic Lyapunov function
k-sample variation
Non quadratic Lyapunov function
k-sample variation
HAL domain(s) :
Sciences de l'ingénieur [physics]/Automatique / Robotique
English abstract : [en]
This work deals with relaxed conditions for stability and stabilization of discrete-time Takagi–Sugeno (TS) models. It recalls classical results found in the literature which use quadratic Lyapunov functions leading to ...
Show more >This work deals with relaxed conditions for stability and stabilization of discrete-time Takagi–Sugeno (TS) models. It recalls classical results found in the literature which use quadratic Lyapunov functions leading to very conservative conditions, and various extensions based on piecewise and non-quadratic Lyapunov functions. Afterwards, a new and powerful way to enhance the previous results is depicted. The basic idea is that waiting long enough a stable model will converge towards its equilibrium and, therefore, the Lyapunov functions under consideration are not necessarily decreasing at every sample, but are allowed to decrease every k samples. Whatever it is k >1, the results are proved to include the standard one-sample case. The potential of this approach is shown through several examples in the paper.Show less >
Show more >This work deals with relaxed conditions for stability and stabilization of discrete-time Takagi–Sugeno (TS) models. It recalls classical results found in the literature which use quadratic Lyapunov functions leading to very conservative conditions, and various extensions based on piecewise and non-quadratic Lyapunov functions. Afterwards, a new and powerful way to enhance the previous results is depicted. The basic idea is that waiting long enough a stable model will converge towards its equilibrium and, therefore, the Lyapunov functions under consideration are not necessarily decreasing at every sample, but are allowed to decrease every k samples. Whatever it is k >1, the results are proved to include the standard one-sample case. The potential of this approach is shown through several examples in the paper.Show less >
Language :
Anglais
Popular science :
Non
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