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- Title
study of the projective transformation under the bilinear strict equivalence.
- Authors
Kalogeropoulos, Grigoris I; Karageorgos, Athanasios D; Pantelous, Athanasios A
- Abstract
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, |$S\left ({F,G} \right)$| , $$\begin{align*} & S\left({F,G}\right): F\dot{x}(t) = G{x}(t) \left(\text{or the dual, } F{x}(t) = G\dot{x}(t)\right), \end{align*}$$ and $$\begin{align*} & S\left({F,G}\right): Fx_{k+1} = Gx_k \left(\text{or the dual, } Fx_k=Gx_{k+1}\right)\!, F,G \in{\mathbb{C}^{m \times n}}, \end{align*}$$ and their properties can be characterized by homogeneous matrix pencils, |$sF - \hat{s}G$|. 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 |${\mathbb{C}^{k \times 2}}$| (for |$k \geqslant 3$| with all |$2\times 2$| -minors non-zero) under the extended Hermite equivalence , in the context of the bilinear strict equivalence relation, a novel projective transformation is analytically derived.
- Subjects
LINEAR time invariant systems; MATRIX pencils; BILINEAR forms; NUMBER systems
- Publication
IMA Journal of Mathematical Control & Information, 2022, Vol 39, Issue 2, p383
- ISSN
0265-0754
- Publication type
Article
- DOI
10.1093/imamci/dnaa039