An approximation theory or strongly stabilizing solutions to the operator LQ Riccati equation

JC Oostveen*, RF Curtain, K Ito

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    8 Citations (Scopus)


    The linear-quadratic (LQ) control problem is considered for a class of infinite-dimensional systems with bounded input and output operators, that are not exponentially stabilizable, but only strongly stabilizable. A sufficient condition for the existence of a minimizing control and of a stabilizing solution to the associated LQ Riccati equation is given. The main contribution of this paper is the convergence of the stabilizing solutions of a sequence of finite-dimensional Riccati equations to the strongly stabilizing solution of the infinite-dimensional Riccati equation. The result is applied to a model of propagation of sound waves in a one-dimensional wave-guide.

    Original languageEnglish
    Pages (from-to)1909-1937
    Number of pages29
    JournalSIAM Journal on Control and Optimization
    Issue number6
    Publication statusPublished - 4-Aug-2000


    • linear quadratic control problem
    • algebraic Riccati equation on Hilbert space
    • dissipative systems
    • collocated actuators and sensors

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