Transfer functions for infinite-dimensional systems

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    In this paper, we study three definitions of the transfer function for an infinite-dimensional system. The first one defines the transfer function as the expression $C(sI-A)^{-1}B+D$. In the second definition, the transfer function is defined as the quotient of the Laplace transform of the output and input, with initial condition zero. In the third definition, we introduce the transfer function as the quotient of the input and output, when the input and output are exponentials. We show that these definitions always agree on the right-half plane bounded to the left by the growth bound of the underlying semigroup, but that they may differ elsewhere.
    Original languageUndefined
    Article number10.1016/j.sysconle.2004.02.002
    Pages (from-to)247-255
    Number of pages9
    JournalSystems and control letters
    Issue number3-4
    Publication statusPublished - Jul 2004


    • EWI-16804
    • MSC-93B99
    • MSC-93C25
    • IR-69933
    • Transfer function
    • METIS-219889
    • Infinite-dimensional system

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