Boundary Control for a Kind of Coupled PDE-ODE System - Yuanting Wang; Fucheng Liao; Yonglong Liao; Zhengwei Shen (Journal of Control Science and Engineering)
A coupled system of an ordinary differential equation (ODE) and a heat partial differential equation (PDE) with spatially varying coefficients is discussed. By using the PDE backstepping method, the state-feedback stabilizing controller is explicitly constructed with the assumptions λ(x)∈P[x]n and λ(x)∈C[0, l]∞, respectively. The closed-loop system is proved to be exponentially stable by this controller. A simulation example is presented to illustrate the effectiveness of the proposed method.