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Differential periodic Riccati equations: Existence and uniqueness of nonnegative definite solutions

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Abstract

In this paper we consider the differential periodic Riccati equation. All the periodic nonnegative definite solutions are characterized in the more general case, providing a method for constructing them. The method is obtained from the study of the invariant subspaces of the monodromy matrix of the associated Hamiltonian system, and from the relations between these invariant subspaces and the controllability and unobservability subspaces. Finally, the method is applied to obtain necessary and sufficient conditions for the existence of any periodic nonnegative definite solution and to study the existence and uniqueness of minimal, maximal, stabilizing, and strong solutions.

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Authors and Affiliations

  1. Dpto. Matemática Aplicada, EU. de Informática, Universidad Politécnica de Valencia, Apartado de Correos 22.012, 46080, Valencia, España

    Antonio Pastor

  2. Dpto. Sistemas Informáticos y Computación, Facultad de Informática, Universidad Politécnica de Valencia, Apartado de Correos 22.012, 46080, Valencia, España

    Vicente Hernández

Authors
  1. Antonio Pastor
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  2. Vicente Hernández
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Additional information

This work has been partially supported by Spanish DGICYT Grant No. PB91-O535.

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Pastor, A., Hernández, V. Differential periodic Riccati equations: Existence and uniqueness of nonnegative definite solutions. Math. Control Signal Systems 6, 341–362 (1993). https://doi.org/10.1007/BF01211501

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  • DOI: https://doi.org/10.1007/BF01211501

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