New bounds for the support of input-output equations in differential-algebraic systems
Abstract
Given a polynomial dynamical system x'=f(x,u) together with an observation function y=g(x,u), where x=(x1,…,xn), u=(u1,…,um) and y are differential variables, and f=(f1,…,fn), g are polynomials with coefficients in a differential field, we study the problem of determining a minimal polynomial differential equation satisfied by the inputs u and the output y which follows as a differential consequence of the system. We provide a characterization of a finite superset of the set of monomials appearing with non-zero coefficients in this input-output equation. Specifically, we establish an upper bound for the degree of the minimal polynomial and a family of inequalities that define a polytope containing its Newton polytope. These results extend recent work by Mukhina and Pogudin for systems with constant parameters, and enable the use of evaluation-interpolation techniques for the efficient computation of such eliminant polynomials.
Related
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BibTeX
@misc{jeronimo2026bounds,
title = {{New bounds for the support of input-output equations in differential-algebraic systems}},
author = {Gabriela Jeronimo and Leonardo Lanciano},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03828},
eprint = {2609.03828},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03828},
}
RIS
TY - UNPB
TI - New bounds for the support of input-output equations in differential-algebraic systems
AU - Gabriela Jeronimo
AU - Leonardo Lanciano
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03828
UR - https://arxiv.org/abs/2609.03828
AB - Given a polynomial dynamical system x'=f(x,u) together with an observation function y=g(x,u), where x=(x_1,…,x_n), u=(u_1,…,u_m) and y are differential variables, and f=(f_1,…,f_n), g are polynomials with coefficients in a differential field, we study the problem of determining a minimal polynomial differential equation satisfied by the inputs u and the output y which follows as a differential consequence of the system. We provide a characterization of a finite superset of the set of monomials appearing with non-zero coefficients in this input-output equation. Specifically, we establish an upper bound for the degree of the minimal polynomial and a family of inequalities that define a polytope containing its Newton polytope. These results extend recent work by Mukhina and Pogudin for systems with constant parameters, and enable the use of evaluation-interpolation techniques for the efficient computation of such eliminant polynomials.
ER -