On the Yakubovich frequency theorem for linear non-autonomous control processes

Roberta Fabbri; Russell Johnson; Carmen Núñez

doi:10.3934/dcds.2003.9.677

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2003, Volume 9, Issue 3: 677-704. Doi: 10.3934/dcds.2003.9.677

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On the Yakubovich frequency theorem for linear non-autonomous control processes

1.
Università di Firenze, Dipartimento di Sistemi e Informatica, Via Santa Marta 3, 50139 Firenze
2.
Dipartimento di Sistemi e Informatica, Università di Firenze, 50139 Firenze
3.
Universidad de Valladolid, Departamento de Matemática Aplicada, ETSII, Paseo del Cauce s/n, 47011 Valladolid

Received: November 30, 2001

Revised: October 31, 2002

Published: April 2003

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Abstract

Using methods of the theory of nonautonomous linear differential systems, namely exponential dichotomies and rotation numbers, we generalize some aspects of Yakubovich's Frequency Theorem from periodic control systems to systems with bounded uniformly continuous coefficients.

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Mathematics Subject Classification: 37B55, 49N10, 34F05, 93D15.

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