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Nonautonomous Linear-Quadratic Dissipative Control Processes Without Uniform Null Controllability

  • Russell Johnson
  • Sylvia Novo
  • Carmen Núñez
  • Rafael Obaya
Article

Abstract

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.

Keywords

Nonautonomous linear Hamiltonian systems Linear-quadratic control system Dissipativity Abnormal system Rotation number Proper focal point 

Notes

Acknowledgments

Partly supported by MIUR (Italy), by MEC (Spain) under Project MTM2012-30860, and by JCyL (Spain) under Project VA118A12-1.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di FirenzeFirenzeItaly
  2. 2.Departamento de Matemática AplicadaUniversidad de ValladolidValladolidSpain

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