The zero dynamics of linear systems with commensurate delays is studied. The zero dynamics is meant to be the dynamical equation that remains after compelling, by the input of the system, the system output to be identically equal to zero. Conditions are found out allowing to transform the system into a normal form that reveals its zero dynamics. By a straightforward use of the obtained decomposition, the disturbance decoupling problem is solved readily. An explanation is given on how to extend the obtained results to systems with distributed delays. Two examples of physical systems illustrate the effectiveness of the presented study.

中文翻译：

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相称和分布式时滞系统的零动力学范式和干扰解耦

研究了具有相应时滞的线性系统的零动力学。零动力学是指在由系统的输入强制系统输出等于零之后的动力学方程式。找到了条件，可以将系统转换为显示零动态的正常形式。通过直接使用获得的分解，可以轻松解决干扰解耦问题。给出了有关如何将获得的结果扩展到具有分布式延迟的系统的解释。物理系统的两个例子说明了所提出研究的有效性。