中文摘要：

本文研究二阶动力学系统的高阶比例积分（PI）观测器设计问题．基于Sylvester矩阵方程的解，提出了该观测器设计的参数化方法．该参数化方法给出了该类观测器增益矩阵的参数化表达式，其所含参数除了满足两个约束条件之外是完全自由的．这些参数为控制系统设计提供了全部自由度，可通过优化等手段选择这些参数来满足某些性能要求，如干扰解耦、故障检测和鲁棒性等．此外，该PI观测器的参数化设计方法直接利用二阶动力学系统的原始参数矩阵，只涉及二阶动力学系统n维参数矩阵的运算．给出一个数值例子，以说明所提方法的简单性和有效性．

英文摘要：

Design of a high-order proportional plus integral （PI） observer in aecond-order dynamic systems is investigated. Based on the solutions to Sylvester matrix equations, a parametric method for designing this observer is proposed. The method presents the parametric expression for the gain matrix of the high-order PI observer. The con- tained parameters satisfy the needs of two constraints and are completely free as well. These parameters offer all the design degrees of freedom, which can be further selected to satisfy certain performances by means of optimization, such as disturbance decoupling, fault detection and robustness. In addition, the parametric method of designing the PI observers directly utilizes the original parameter matrices of the second-order dynamic systems and involves manipu- lations only on n-dimensional matrices of the second-order dynamic systems. A numerical example is presented to show the simplicity and effectiveness of the proposed method.