Connections between the algebraic Riccati equation and the Hamiltonian for Riesz-spectral systems

C.R. Kuiper, H.J. Zwart

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    Abstract

    The algebraic Riccati equation (ARE) has been studied in great detail for finite-dimensional systems. For infinite-dimensional systems almost all results concentrate on the relation with the linear quadratic optimal control problem. The object of this paper is to consider solutions of the ARE for infinite-dimensional systems from a more general point of view. The relation between linear, bounded solutions of the ARE and the eigenvectors of the Hamiltonian will be studied, in the case when the Hamiltonian is a Riesz-spectral operator. We present a general form of all possible linear, bounded solutions of the ARE in terms of the eigenvectors of the Hamiltonian. Characterizations for self-adjoint, nonnegative and stabilizing solutions are given as well. The derived results shall be applied to the heat equation.
    Original languageEnglish
    Number of pages48
    JournalJournal of mathematical systems, estimation and control
    Volume6
    Issue number4
    Publication statusPublished - 1996

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