Clocks and Insensitivity to Small Measurement Errors

Free access article

Issue		ESAIM: COCV Volume 4, 1999


Page(s)		537 - 557
DOI		10.1051/cocv:1999121

DOI: 10.1051/cocv:1999121

ESAIM: COCV, October 1999, Vol. 4, p. 537-557

Clocks and Insensitivity to Small Measurement Errors

Horloges et insensibilité à de petites erreurs de mesure

Eduardo D. Sontag
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, U.S.A.; (sontag@hilbert.rutgers.edu)

Received February 26, 1999. Revised September 4, 1999.

Abstract: This paper deals with the problem of stabilizing a system in the presence of small measurement errors. It is known that, for general stabilizable systems, there may be no possible memoryless state feedback which is robust with respect to such errors. In contrast, a precise result is given here, showing that, if a (continuous-time, finite-dimensional) system is stabilizable in any way whatsoever (even by means of a dynamic, time varying, discontinuous, feedback) then it can also be semiglobally and practically stabilized in a way which is insensitive to small measurement errors, by means of a hybrid strategy based on the idea of sampling at a "slow enough'' rate.

Résumé: Cet article traite du problème de la stabilisation d'un système en présence de petites erreurs de mesure. Il est connu que, pour des systèmes stabilisables généraux, il ne peut pas exister de feedback d'état sans mémoire qui soit résistant à de telles erreurs. À l'opposé, un résultat précis est donné ici, montrant que, si un système (en temps continu et dimension finie) est stabilisable d'une quelconque façon (même à l'aide d'un feedback dynamique, instationnaire, discontinu), alors il peut être semi-globalement et pratiquement stabilisé d'une façon insensible à de petites erreurs de mesure, à l'aide d'une stratégie hybride reposant sur l'idée d'une prise de mesure de l'état à un rythme suffisamment lent.

Keywords and phrases: Control systems, feedback stabilization, controllability.

AMS Subject Classification: 93B52, 93D15.

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