Stabilization of coupled pde-ode systems with spatially varying coefficient

The paper is concerned with the stabilization of a class of coupled PDE-ODE systems with spatially varying coefficient, via state-feedback or output-feedback. The system is more general than that of the related literature due to the presence of the spatially varying coefficient which makes the problem more difficult to solve. By infinite-dimensional backstepping method, both state-feedback and output-feedback stabilizing controllers are explicitly constructed, which guarantee that the closed-loop system is exponentially stable in the sense of certain norm. It is worthwhile pointing out that, in the case of output-feedback, by appropriately choosing the state observer gains, the severe restriction on the ODE sub-system in the existing results is completely removed. A simulation example is presented to illustrate the effectiveness of the proposed method.