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    A reduction technique for discrete generalized algebraic and difference Riccati equations

    193096_193096.pdf (165.9Kb)
    Access Status
    Open access
    Authors
    Ferrante, A.
    Ntogramatzidis, Lorenzo
    Date
    2013
    Type
    Journal Article
    
    Metadata
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    Citation
    Ferrante, Augusto and Ntogramatzidis, Lorenzo. 2013. A reduction technique for discrete generalized algebraic and difference Riccati equations. Linear and Multilinear Algebra. 62 (11): pp. 1460-1474.
    Source Title
    Linear and Multilinear Algebra
    DOI
    10.1080/03081087.2013.834056
    ISSN
    0308-1087
    URI
    http://hdl.handle.net/20.500.11937/9318
    Collection
    • Curtin Research Publications
    Abstract

    This paper proposes a reduction technique for the generalized Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalized discrete algebraic Riccati equation. In particular, an analysis on the eigenstructure of the corresponding extended symplectic pencil enables to identify a subspace in which all the solutions of the generalized discrete algebraic Riccati equation are coincident. This subspace is the key to derive a decomposition technique for the generalized Riccati difference equation. This decomposition isolates a “nilpotent” part, which converges to a steady-state solution in a finite number of steps, from another part that can be computed by iterating a reduced-order generalized Riccati difference equation.

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