Abstract
It is well known that for infinite-dimensional systems, exponential stability is not necessarily determined by the location of its spectrum. Similarly, a transfer function in H ∞(ℂ+) need not have an exponentially stable realization. This paper addresses this problem for a class of impulse responses called pseudorational. In this class, it is shown that the difficulty is related to classical complex analysis, in particular that of entire functions of finite order. The infinite-product representation for entire functions makes it possible to prove that stability is indeed determined by the location of the spectrum.
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© 1990 Birkhäuser Boston
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Yamamoto, Y. (1990). Correspondence of Internal and External Stability — Realization, Transfer Functions and Complex Analysis. In: Kaashoek, M.A., van Schuppen, J.H., Ran, A.C.M. (eds) Realization and Modelling in System Theory. Progress in Systems and Control Theory, vol 3. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3462-3_5
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DOI: https://doi.org/10.1007/978-1-4612-3462-3_5
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