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.

翻译：本技术报告通过一个反例表明，Geng等人（IEEE Trans. Automat. Control, 2024）所提出的等价条件——即使用最小阶补偿器（MOC）来实现期望设计（包括广义正则性或同时满足广义正则性与无脉冲性）——是充分但非必要的。此外，本文引入了修正的等价条件，以及一个确保闭环系统在使用MOC时保持广义正则、无脉冲且稳定的等价条件。同时，研究表明输出反馈可以替代MOC，在不增加系统维度的前提下实现相同设计。这些结论通过一个电路实例得到了验证。