In this paper, the output feedback stabilization problem is studied for a class of cascade nonlinear ODE-PDE systems. The nonlinear terms of ODE-subsystem are assumed to be bounded by a known constant multiplied by unmeasured states, and PDE-subsystem is a diffusion equation. Especially, the unstable diffusion equation is considered. Based on the low gain observer and a series of transformations, the output feedback stabilization problem is converted into designing proper gain parameters. Furthermore, the stability of the closed-loop system is analyzed by Lyapunov theorem. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed control strategy.

本文研究了一类级联非线性ODE-PDE系统的输出反馈镇定问题。假设 ODE 子系统的非线性项以已知常数乘以未测量状态为界，而 PDE 子系统是一个扩散方程。特别地，考虑了不稳定的扩散方程。基于低增益观测器和一系列变换，输出反馈稳定问题转化为设计合适的增益参数。此外，利用李雅普诺夫定理分析了闭环系统的稳定性。最后，给出了两个数值例子来证明所提出的控制策略的有效性。