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    On the generalized algebraic Riccati equations

    Access Status
    Fulltext not available
    Authors
    Ferrante, A.
    Ntogramatzidis, Lorenzo
    Date
    2017
    Type
    Journal Article
    
    Metadata
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    Citation
    Ferrante, A. and Ntogramatzidis, L. 2017. On the generalized algebraic Riccati equations. IFAC-PapersOnLine. 50 (1): pp. 9555-9560.
    Source Title
    IFAC-PapersOnLine
    DOI
    10.1016/j.ifacol.2017.08.1653
    ISSN
    2405-8963
    School
    Department of Mathematics and Statistics
    Funding and Sponsorship
    http://purl.org/au-research/grants/arc/DP160104994
    URI
    http://hdl.handle.net/20.500.11937/58801
    Collection
    • Curtin Research Publications
    Abstract

    Three hundred years have passed since Jacopo Francesco Riccati analyzed a quadratic differential equation that would have been of crucial importance in many fields of engineering and applied mathematics. Indeed, countless variations and generalizations of this equation have been considered as they proved to be the right mathematical tool to address important problems. This paper is focused on a generalized version of the matrix Riccati equation where the matrix that in the classical Riccati equation is inverted can be singular: we analyze the equation obtained by substituting the inverse operator with the Moore-Penrose pseudo-inverse. The equations obtained by this substitution are known as generalized Riccati equations. The relation between these equations — both in continuos-time and in discrete-time — and singular Linear Quadratic (LQ) optimal control problem are examined. A geometric characterization of the set of solutions of the generalized Riccati equation is illustrated. It is shown that in this general setting there are LQ optimal control problems for which the optimal closed-loop system is stable also in cases where the Riccati equation does not possess a stabilizing solution.

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