Abstract
An inverse realization problem is solved for a class of analytic functions: Given a function, find a regular differential polynomial that annihilates it. It is shown that the minimal annihilator has degree \(m+1\), where m is the highest multiplicity of the zeros of x belonging to a class of analytic functions. This generalizes the realization of Bohl functions as solutions to LTI-ODE’s. With it, the unit solution of the scale-delay equation (SDE) is approximated as the solution to a second-order time-variant ODE. Some new identities for the exact zeros of the SDE are proven.
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The support by the NSF grant CPS-1544857 is gratefully acknowledged.
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Verriest, E.I. (2021). Properties of the Zeros of the Scale-Delay Equation and Its Time-Variant ODE Realization. In: Kilgour, D.M., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Developments in Mathematical, Statistical and Computational Sciences. AMMCS 2019. Springer Proceedings in Mathematics & Statistics, vol 343. Springer, Cham. https://doi.org/10.1007/978-3-030-63591-6_10
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