The aim of this paper is to show the applicability of geometric techniques to a regulation problem for linear, time-delay systems. Given a plant whose dynamics equations include delays and an exosystem that generates a reference signal, the problem we consider consists in finding a feedback regulator which guarantees asymptotic stability of the regulation loop and asymptotic command following of the reference signal, for any initial condition of the overall system in the presence of disturbances. By associating to the time-delay plant a corresponding abstract system with coefficients in a ring, it is possible to place our investigation in a finite dimensional algebraic context, where intuition and results obtained in the classical case, that is without delays, may be exploited. In particular, using tools and methods of the geometricapproach to systems with coefficients in a ring, sufficient conditions for the solvability of the considered problem are found and a constructive procedure, which works under specific hypotheses, is given.

A geometric approach to the general autonomous regulator problem in the time-delay framework

CONTE, GIUSEPPE;PERDON, ANNA MARIA;
2012-01-01

Abstract

The aim of this paper is to show the applicability of geometric techniques to a regulation problem for linear, time-delay systems. Given a plant whose dynamics equations include delays and an exosystem that generates a reference signal, the problem we consider consists in finding a feedback regulator which guarantees asymptotic stability of the regulation loop and asymptotic command following of the reference signal, for any initial condition of the overall system in the presence of disturbances. By associating to the time-delay plant a corresponding abstract system with coefficients in a ring, it is possible to place our investigation in a finite dimensional algebraic context, where intuition and results obtained in the classical case, that is without delays, may be exploited. In particular, using tools and methods of the geometricapproach to systems with coefficients in a ring, sufficient conditions for the solvability of the considered problem are found and a constructive procedure, which works under specific hypotheses, is given.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/71840
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 6
social impact