TY - JOUR
T1 - The study of the projective transformation under the bilinear strict equivalence
AU - Kalogeropoulos, Grigoris I.
AU - Karageorgos, Athanasios D.
AU - Pantelous, Athanasios A.
N1 - Publisher Copyright:
© 2020 The Author(s) 2020. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
PY - 2022/6
Y1 - 2022/6
N2 - The study of linear time invariant descriptor systems has intimately been related to the study of matrix pencils. It is true that a large number of systems can be reduced to the study of differential (or difference) systems, S(F,G),S(F,G):Fx˙(t)=Gx(t)(or the dual, Fx(t)=Gx˙(t)),andS(F,G):Fxk+1=Gxk(or the dual, Fxk=Gxk+1),F,G∈Cm×n,and their properties can be characterized by homogeneous matrix pencils, sF−s^G. Based on the fact that the study of the invariants for the projective equivalence class can be reduced to the study of the invariants of the matrices of set Ck×2 (for k⩾3 with all 2×2-minors non-zero) under the extended Hermite equivalence, in the context of the bilinear strict equivalence relation, a novel projective transformation is analytically derived.
AB - The study of linear time invariant descriptor systems has intimately been related to the study of matrix pencils. It is true that a large number of systems can be reduced to the study of differential (or difference) systems, S(F,G),S(F,G):Fx˙(t)=Gx(t)(or the dual, Fx(t)=Gx˙(t)),andS(F,G):Fxk+1=Gxk(or the dual, Fxk=Gxk+1),F,G∈Cm×n,and their properties can be characterized by homogeneous matrix pencils, sF−s^G. Based on the fact that the study of the invariants for the projective equivalence class can be reduced to the study of the invariants of the matrices of set Ck×2 (for k⩾3 with all 2×2-minors non-zero) under the extended Hermite equivalence, in the context of the bilinear strict equivalence relation, a novel projective transformation is analytically derived.
KW - bilinear-strict equivalence
KW - extended Hermite Equivalence
KW - linear systems
KW - matrix pencil theory
UR - https://www.scopus.com/pages/publications/85133735289
U2 - 10.1093/imamci/dnaa039
DO - 10.1093/imamci/dnaa039
M3 - Article
AN - SCOPUS:85133735289
SN - 0265-0754
VL - 39
SP - 383
EP - 408
JO - IMA Journal of Mathematical Control and Information
JF - IMA Journal of Mathematical Control and Information
IS - 2
ER -