This article studies the parametric design of reduced-order functional observer (ROFO) for linear time-varying (LTV) systems. Firstly, existence conditions of the ROFO are deduced based on the differentiable nonsingular transformation. Then, depending on the solution of the generalized Sylvester equation (GSE), a series of fully parameterized expressions of observer coefficient matrices are established, and a parametric design flow is given. Using this method, the observer can be constructed under the expected convergence speed of the observation error. Finally, two numerical examples are given to verify the correctness and effectiveness of this method and also the aircraft control problem.

本文研究线性时变 (LTV) 系统的降阶函数观测器 (ROFO) 的参数化设计。首先，基于可微非奇异变换推导出ROFO的存在条件。然后，根据广义西尔维斯特方程(GSE)的解，建立了一系列观测器系数矩阵的全参数化表达式，并给出了参数化设计流程。使用这种方法，可以在观测误差的预期收敛速度下构造观测器。最后通过两个数值算例验证了该方法的正确性和有效性以及飞机控制问题。