Stabilization of Coupled ODE‐PDE System with Intermediate Point and Spatially Varying Effects Interconnection

Abstract In this paper, the stabilization analysis problem of a bi‐directional coupled ODE‐PDE system is proposed. The spatially varying coefficient and the intermediate point interaction between the subsystems makes the coupled system more representative. An invertible infinite‐dimensional backstepping transformation is introducted to bring the original system into an exponentially stable target system. By employing the backstepping method, the kernel functions in the transformations are worked out under some assumptions of the spatially varying coefficient. Then, an explicit state‐feedback law is designed and the exponential stability of the transformed closed‐loop system has been also discussed. Finally, numerical simulation is provided to illustrate the effectiveness of the proposed design.