Robust stabilization of discrete-time periodic linear systems for tracking and disturbance rejection - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematics of Control, Signals, and Systems Année : 2016

Robust stabilization of discrete-time periodic linear systems for tracking and disturbance rejection

Résumé

In analogy to the Kučera-Youla parametrization, we construct and para-metrize all stabilizing controllers of a stabilizable linear periodic discrete-time input/output system, the plant. We establish a necessary and sufficient algebraic condition for the existence of controllers among these for which the output of the plant tracks a given reference signal in spite of disturbance signals on the input and the output of the plant. With a minor additional assumption, the tracking stabilizing controllers are robust. As in the linear time-invariant (LTI) case, the reference and disturbance signals are assumed to be generated by an autonomous system. Our results are the analogs for periodic behaviors of the corresponding LTI results of Vidyasagar. A completely different approach to stabilization and control of discrete periodic systems was developed by Bittanti and Colaneri. We derive a categorical duality between periodic behaviors over the time-axis of natural numbers and finitely generated modules over a suitable noncommutative ring of difference operators and use this for the proof of the main stabilization and control results. Morita's theory of equivalences between module categories is employed as an essential algebraic tool. All results of the paper are constructive.
Fichier principal
Vignette du fichier
R53bis.pdf (280.99 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02367980 , version 1 (20-11-2019)

Identifiants

Citer

Henri Bourlès, Ulrich Oberst. Robust stabilization of discrete-time periodic linear systems for tracking and disturbance rejection. Mathematics of Control, Signals, and Systems, 2016, 28, pp.1-34. ⟨10.1007/s00498-016-0171-8⟩. ⟨hal-02367980⟩
52 Consultations
99 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More