A Hyperbolic PDE-ODE System with Delay-Robust Stabilization

Abstract

This paper is concerned with a new development of a delay-robust stabilizing feedback control law for linear ordinary differential equation coupled with two linear first order hyperbolic equations in the actuation path. A second change of variables that reduce stabilization problem of the PDE-ODE system to that of a time-delay system for which a forecaster can be constructed. Hence, by choosing the pole placement on the ODE when constructing the forecaster, enabling a trade-off between convergence rate and delay-robustness. The proposed feedback law is finally proved to be robust to small delays in the actuation.