Journal of Dynamics and Differential Equations

, Volume 25, Issue 3, pp 679–713 | Cite as

Dynamical Methods for Linear Hamiltonian Systems with Applications to Control Processes

Article
First Online:
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Abstract

The nonautonomous version of the Yakubovich Frequency Theorem characterizes the solvability of an infinite horizon optimization problem in terms of the validity of the Frequency and Nonoscillation Conditions for a linear Hamiltonian system, which is defined from the coefficients of the quadratic functional to be minimized. This paper describes those nonautonomous linear Hamiltonian systems satisfying the required properties. Two groups appear, depending on whether they are uniformly weakly disconjugate or not. It also contains a previous analysis of the long-term behavior of the Grassmannian and Lagrangian flows under the presence of exponential dichotomy, which is required for the classification and has interest by itself.

Keywords

Nonautonomous linear Hamiltoniam systems Grassmmanian and Lagrangian flows Monotonicity properties of the Riccati equations Optimization of quadratic functionals Frequency and nonoscillation conditions Uniform weak disconjugacy 

Mathematics Subject Classification (1991)

37B55 37J05 49N10 
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Notes

Acknowledgments

This research partly supported by GNAMPA and MURST (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 2013

Authors and Affiliations

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

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