Open AccessAlgebraic analysis of the structural properties of parametric linear time‐invariant systems
Author(s) -
Menini Laura,
Possieri Corrado,
Tornambè Antonio
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2020.0783
Subject(s) - observability , reachability , controllability , lti system theory , algebraic number , linear system , parametric statistics , mathematics , invariant (physics) , discrete time and continuous time , control theory (sociology) , algebra over a field , computer science , algorithm , pure mathematics , mathematical analysis , statistics , control (management) , artificial intelligence , mathematical physics
By using techniques borrowed from algebraic geometry, some tests are proposed to certify structural properties (such as reachability, observability, controllability, constructibility, stabilisability, and detectability) of discrete‐time and continuous‐time linear time‐invariant systems. These results are then generalised for linear time‐invariant systems depending polynomially on some real parameters, by exploiting the notion of Gröbner cover. The main innovation of the proposed results with respect to existing techniques is that they provide exact certificates for the structural properties of linear time‐invariant systems. Examples of application are given all throughout the study to illustrate and validate the theoretical results.