Nonautonomous linear-quadratic dissipative control processes without uniform null controllability
- Johnson, Russell
- Novo Martín, Sylvia
- Núñez Jiménez, María del Carmen
- Obaya García, Rafael
ISSN: 1040-7294
ISBN: 10884-015-9495-1
Année de publication: 2017
Pages: 355-383
Type: Article
D'autres publications dans: Journal of Dynamics and Differential Equations
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Résumé
In this paper the dissipativity of a family of linear-quadratic control processes is studied. The application of the Pontryagin Maximum Principle to this problem gives rise to a family of linear Hamiltonian systems for which the existence of an exponential dichotomy is assumed, but no condition of controllability is imposed. As a consequence, some of the systems of this family could be abnormal. Sufficient conditions for the dissipativity of the processes are provided assuming the existence of global positive solutions of the Riccati equation induced by the family of linear Hamiltonian systems or by a convenient disconjugate perturbation of it.