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Optimal input-output stabilization of infinite-dimensional discrete time-invariant linear systems by output injection


Reference:

Opmeer, M. R. and Staffans, O. J., 2010. Optimal input-output stabilization of infinite-dimensional discrete time-invariant linear systems by output injection. SIAM Journal on Control and Optimization (SICON), 48 (8), pp. 5084-5107.

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    Official URL:

    http://dx.doi.org/10.1137/090762233

    Abstract

    We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by output injection. We show that a necessary and sufficient condition for this problem to be solvable is that the transfer function has a left factorization over H-infinity. Another equivalent condition is that the filter Riccati equation (of an arbitrary realization) has a solution (in general, unbounded and even nondensely defined). We further show that after renorming the state space in terms of the inverse of the smallest solution of the filter Riccati equation, the closed-loop system is not only input-output stable but also strongly internally *-stable.

    Details

    Item Type Articles
    CreatorsOpmeer, M. R.and Staffans, O. J.
    DOI10.1137/090762233
    Uncontrolled Keywordsinfinite-dimensional system, input-output stabilization, linear quadratic optimal control, riccati equation, left factorization, output injection
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher StatementOpmeer_SICON_2010_48_8_5084.pdf: © 2010 Society for Industrial and Applied Mathematics
    RefereedYes
    StatusPublished
    ID Code22890

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