Year: 2026
Type: preprint
Abstract: We study the complexity of minimal positive realization for discrete-time systems. We prove that, given a strictly proper transfer matrix with rational coefficients and an order bound encoded in unary, deciding whether a positive realization exists within that bound is complete for the existential theory of the reals. We further prove hardness for stable single-input single-output transfer functions that admit positive realizations, even when the bound equals the McMillan degree.
Source: arXiv (Cornell University)
Author: Liu, Zhaobo
Institution: Shenzhen University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G2158150094, G5283841727
OpenAlex ID: W7221330690