Canonical State Space Realizations of IO Systems via Gröbner Bases

2020 ◽  
pp. 655-720
Author(s):  
Ulrich Oberst ◽  
Martin Scheicher ◽  
Ingrid Scheicher
Keyword(s):  
State Space ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Canonical State

scholarly journals An Algebraic Approach to Identifiability

Algorithms ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 255
Author(s):  
Daniel Gerbet ◽  
Klaus Röbenack
Keyword(s):  
Algebraic Geometry ◽  
State Space ◽  
Differential Algebra ◽  
Gröbner Bases ◽  
Algebraic Approach ◽  
Grobner Bases ◽  
Space Systems ◽  
Input Output ◽  
Polynomial Ideals ◽  
State Space Systems

This paper addresses the problem of identifiability of nonlinear polynomial state-space systems. Such systems have already been studied via the input-output equations, a description that, in general, requires differential algebra. The authors use a different algebraic approach, which is based on distinguishability and observability. Employing techniques from algebraic geometry such as polynomial ideals and Gröbner bases, local as well as global results are derived. The methods are illustrated on some example systems.

scholarly journals Gröbner bases for operads

2010 ◽  
Vol 153 (2) ◽  
pp. 363-396 ◽  
Author(s):  
Vladimir Dotsenko ◽  
Anton Khoroshkin
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases

scholarly journals Gröbner bases over fields with valuations

2018 ◽  
Vol 88 (315) ◽  
pp. 467-483 ◽  
Author(s):  
Andrew J. Chan ◽  
Diane Maclagan
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases
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