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.

Menini, L., Possieri, C., Tornambe, A. (2020). Algebraic analysis of the structural properties of parametric linear time-invariant systems. IET CONTROL THEORY & APPLICATIONS, 14(20), 3568-3579 [10.1049/iet-cta.2020.0783].

Algebraic analysis of the structural properties of parametric linear time-invariant systems

Menini L.;Possieri C.;Tornambe A.
2020-01-01

Abstract

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.
2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore ING-INF/04 - AUTOMATICA
English
algebra
discrete time systems
geometry
multidimensional systems
polynomials
continuous time systems
linear systems
algebraic analysis
parametric linear time-invariant systems
algebraic geometry
certify structural properties
Menini, L., Possieri, C., Tornambe, A. (2020). Algebraic analysis of the structural properties of parametric linear time-invariant systems. IET CONTROL THEORY & APPLICATIONS, 14(20), 3568-3579 [10.1049/iet-cta.2020.0783].
Menini, L; Possieri, C; Tornambe, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/294468
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