This paper addresses the output feedback stabilization of an ODE–PDE cascade. The PDE takes the form of a 1-D reaction–diffusion equation. The output of the ODE enters into the PDE via a Dirichlet/Neumann/Robin boundary condition. It is assumed that both the output of the ODE and the output of the PDE, selected as a boundary Dirichlet trace, are available for feedback control. The proposed control strategy takes the form of a finite-dimensional observer-based controller. Under a suitable structural controllability property, we show that the reported control strategy achieves the exponential stabilization of the plant when the order of the observer is selected large enough. We then demonstrate how such a control strategy can be adapted and augmented with a predictor component in order to achieve the stabilization of the above mentioned PDE–ODE cascade when the output of the ODE enters into the PDE with an arbitrarily long delay.

本文讨论了 ODE-PDE 级联的输出反馈稳定性。PDE 采用一维反应-扩散方程的形式。ODE 的输出通过 Dirichlet/Neumann/Robin 边界条件进入 PDE。假设 ODE 的输出和 PDE 的输出都被选为边界 Dirichlet 迹线，可用于反馈控制。所提出的控制策略采用基于有限维观察器的控制器的形式。在合适的结构可控性属性下，我们表明，当观察者的阶数选择得足够大时，所报告的控制策略实现了对象的指数稳定。