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

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May 2003, 9(3): 677-704. doi: 10.3934/dcds.2003.9.677

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

Roberta Fabbri ^1, , Russell Johnson ^2, and Carmen Núñez ^3,

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

Received December 2001 Revised November 2002 Published February 2003

Abstract
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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.

Keywords: exponential dichotomy, rotation number., Frequency Theorem.

Mathematics Subject Classification: 37B55, 49N10, 34F05, 93D1.

Citation: Roberta Fabbri, Russell Johnson, Carmen Núñez. On the Yakubovich frequency theorem for linear non-autonomous control processes. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 677-704. doi: 10.3934/dcds.2003.9.677

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