Comments and extensions on "State-equivalent form and minimum-order compensator design for rectangular descriptor systems"
Abstract
This technical note presents a counterexample showing that the equivalence conditions proposed by Geng et al. (IEEE Trans. Automat. Control, 2024), which use a minimum-order compensator (MOC) to achieve desired designs, including generalized regularity or both generalized regularity and free of impulse, are sufficient but not necessary. Furthermore, revised equivalence conditions are introduced, along with an equivalence condition ensuring the closed-loop system remains generalized regular, impulse-free, and stable using MOC. Additionally, it is shown that output feedback can replace the MOC, achieving the same design without increasing dimensionality. These findings are validated through a circuit example.
Cite
@article{arxiv.2501.13445,
title = {Comments and extensions on "State-equivalent form and minimum-order compensator design for rectangular descriptor systems"},
author = {Shuo Shi and Juan Zhang},
journal= {arXiv preprint arXiv:2501.13445},
year = {2025}
}
Comments
We find a counterexample to illustrate that Theorem 5 (iii) and (iv) are incorrect