Remarks on linear-quadratic dissipative control systems

Russell Johnson; Carmen Núñez

doi:10.3934/dcdsb.2015.20.889

Article Contents

2015, Volume 20, Issue 3: 889-914. Doi: 10.3934/dcdsb.2015.20.889

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Remarks on linear-quadratic dissipative control systems

Russell Johnson^1, and
Carmen Núñez^2,

1.
Dipartimento di Matematica e Informatica, Università di Firenze, Via di Santa Marta 3, 50139 Firenze
2.
Departamento de Matemática Aplicada, E. Ingenierías Industriales, Universidad de Valladolid, Paseo del Cauce 59, 47011 Valladolid

Received: August 2013

Revised: May 2014

Published: May 2015

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Abstract

We study the concept of dissipativity in the sense of Willems for nonautonomous linear-quadratic (LQ) control systems. A nonautonomous system of Hamiltonian ODEs is associated with such an LQ system by way of the Pontryagin Maximum Principle. We relate the concepts of exponential dichotomy and weak disconjugacy for this Hamiltonian ODE to that of dissipativity for the LQ system.

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Mathematics Subject Classification: 37B55, 34C10, 34L05.

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