Comments and extensions on "State-equivalent form and minimum-order compensator design for rectangular descriptor systems"

TL;DR

This paper challenges existing equivalence conditions for minimum-order compensator design in descriptor systems, providing counterexamples, revised conditions, and demonstrating output feedback as an alternative, validated through a circuit example.

Contribution

It introduces revised equivalence conditions for MOC design, shows output feedback can replace MOC, and corrects prior assumptions in descriptor system control design.

Findings

Counterexample disproves sufficiency of previous conditions

Revised conditions ensure desired system properties with MOC

Output feedback can achieve the same design without increasing system order

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.