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 back stepping method, the state-feedback stabilizing controller is explicitly constructed with the assumptions ?(x) ? P[x]n and ?(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.
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