Abstract In this paper, the counterexamples to the general theory related to the state-feedback IMC plants are given and investigated. It is shown, that the maximum-speed multivariable perfect control schemes do not necessitate the maximum-energy of the control input variables. In that way, the IMC peculiarities involving the nonzero perfect control closed-loop poles are indicated, which constitutes a solid counterweight to the well-known general system theory. A new geometric approach results in counterexamples for both full and non-full rank plants, giving rise to the introduction of a complete analytical paradigm in the nearest future. Numerical examples confirm the intriguing issues covering the paper.

中文翻译：

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最大速度/能量 IMC 理论的反例 - 一种新的几何考虑结合了 LTI 离散时间状态空间框架中定义的多变量完美控制

摘要 在本文中，给出并研究了与状态反馈 IMC 设备相关的一般理论的反例。结果表明，最大速度多变量完美控制方案不需要控制输入变量的最大能量。通过这种方式，表明了涉及非零完美控制闭环极点的 IMC 特性，这构成了对众所周知的一般系统理论的坚实平衡。一种新的几何方法产生了满秩和非满秩植物的反例，从而在不久的将来引入了完整的分析范式。数值例子证实了论文中的有趣问题。