带有输出时滞的线性系统的观测器设计

Observer Design for a Linear System with Output Delay

摘要: 本文研究输出带有时滞的线性系统的观测器设计问题。通过将输出时滞写成传播方程的形式，带有输出时滞的观测器设计问题就变成了ODE和传播方程组成的级联系统的观测问题。通过引入新的变换，输出时滞得以有效地补偿。本文给出了观测器的设计过程，并且在观测器的适定性证明中摆脱了Lyapunov函数的构造。最后给出数值仿真说明了观测器的有效性。

Abstract: In this paper, we study the observer design for a linear system with output delay. By writing the time delay as a transport equation, the observer design with output delay can be regarded as the observation problem of a cascade system that consists of an ODE and a transport equation. The output delay can be compensated by introducing a new transformation. The whole process of the observer design is proposed in this paper. Moreover, the construction of Lyapunov function can be avoided in the proof of the well-posedness. Finally, some numerical simulations are given to validate the effectiveness of the observer.