This paper studies the existence conditions for the observer design of general linear time-invariant descriptor systems. A necessary and sufficient condition is established in terms of a simple rank criterion involving system coefficient matrices. The asymptotic observer is realized by using a dynamical system described by ordinary differential equations (ODEs). The developed test condition is more accessible to implement than the other two existing works. Numerical examples are provided to demonstrate the effectiveness of the theoretical results obtained.

中文翻译：

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描述符系统的ODE观测器设计的充要条件

本文研究了一般线性时不变描述符系统的观测器设计的存在条件。根据涉及系​​统系数矩阵的简单等级标准，建立了必要和充分的条件。通过使用由常微分方程（ODE）描述的动力学系统来实现渐近观测器。与其他两个现有工作相比，开发的测试条件更易于实施。数值例子说明了所获得理论结果的有效性。