标题： 具有反应扩散方程的非线性常微分方程的输出反馈扰动到状态稳定化 显示英文标题

标题： Disturbance-to-state stabilization by output feedback of nonlinear ODE cascaded with a reaction-diffusion equation

摘要： 在本文中，我们分析了由$1-d$热扩散方程影响的级联非线性常微分方程的输出稳定化问题，该方程同时受到域内和边界扰动的影响。 我们假设状态的唯一可用部分是常微分方程子系统的第一个组件以及热子系统的其中一个边界。 该系统的特点有两方面：i) 它包含一个非线性加法项在常微分方程子系统中，ii) 它同时受到边界和域内扰动信号的影响。 对于这样的系统，与现有工作不同，我们成功设计了一个基于输出观测器的反馈，不仅保证了渐近稳定结果，还保证了我们级联系统的全局{\it 扰动到状态稳定化}。 输出反馈是通过使用最近为耦合常微分方程-热方程引入的适当反步变换，结合高增益观测器和高增益控制器来设计的。 显示英文摘要

摘要： In this paper, we analyze the output stabilization problem for cascaded nonlinear ODE with $1-d$ heat diffusion equation affected by both in-domain and boundary perturbations. We assume that the only available part of states is the first components of the ODE-subsystem and one boundary of the heat-subsystem. The particularity of this system is two folds i) it contains a nonlinear additive term in the ODE-subsystem, and ii) it is affected by both boundary and in-domain perturbations signals. For such a system, and unlike the existing works, we succeeded to design an output observer-based feedback that guarantees not only asymptotic stabilization result but also a globally {\it disturbance-to-state stabilization} for our cascaded system. The output feedback is designed using an adequate backstepping transformation recently introduced for coupled ODE-heat equations combined with high-gain observer and high-gain controller.