Abstract
The problem of finding a minimal realization of a single-input single-output nonlinear retarded time-delay input-output equation with constant commensurable delays is addressed. First, an algorithm is given to find an observable realization of dimension <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -th order input-output equation. Then, this algorithm is modified under two technical assumptions to find a realization of lower dimension, which is observable and accessible. It is shown that under the same technical assumptions an observable and accessible realization has minimal possible state-space dimension among all possible realizations. An algebraic approach based on polynomial tools and modules of differential 1-forms is used to derive the results.
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