Output feedback stabilization of an ODE-Reaction–Diffusion PDE cascade with a long interconnection delay

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