On real and observable rational realizations of input-output equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912268444237824 |
|---|---|
| author | Falkensteiner, Sebastian Pavlov, Dmitrii Sendra, Rafael |
| author_facet | Falkensteiner, Sebastian Pavlov, Dmitrii Sendra, Rafael |
| contents | Given a single (differential-algebraic) input-output equation, we present a method for finding different representations of the associated system in the form of rational realizations; these are dynamical systems with rational right-hand sides. It has been shown that in the case where the input-output equation is of order one, rational realizations can be computed, if they exist. In this work, we focus first on the existence and actual computation of the so-called observable rational realizations, and secondly on rational realizations with real coefficients. The study of observable realizations allows to find every rational realization of a given first order input-output equation, and the necessary field extensions in this process. We show that for first order input-output equations the existence of a rational realization is equivalent to the existence of an observable rational realization. Moreover, we give a criterion to decide the existence of real rational realizations. The computation of observable and real realizations of first order input-output equations is fully algorithmic. We also present partial results for the case of higher order input-output equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16799 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On real and observable rational realizations of input-output equations Falkensteiner, Sebastian Pavlov, Dmitrii Sendra, Rafael Symbolic Computation Algebraic Geometry Dynamical Systems Optimization and Control 93B15, 93B07, 14H50, 34H05 Given a single (differential-algebraic) input-output equation, we present a method for finding different representations of the associated system in the form of rational realizations; these are dynamical systems with rational right-hand sides. It has been shown that in the case where the input-output equation is of order one, rational realizations can be computed, if they exist. In this work, we focus first on the existence and actual computation of the so-called observable rational realizations, and secondly on rational realizations with real coefficients. The study of observable realizations allows to find every rational realization of a given first order input-output equation, and the necessary field extensions in this process. We show that for first order input-output equations the existence of a rational realization is equivalent to the existence of an observable rational realization. Moreover, we give a criterion to decide the existence of real rational realizations. The computation of observable and real realizations of first order input-output equations is fully algorithmic. We also present partial results for the case of higher order input-output equations. |
| title | On real and observable rational realizations of input-output equations |
| topic | Symbolic Computation Algebraic Geometry Dynamical Systems Optimization and Control 93B15, 93B07, 14H50, 34H05 |
| url | https://arxiv.org/abs/2303.16799 |