Stabilization for boundary controlled cascaded heat-ODE system with time-dependent coefficient

In this paper, the stabilization of a cascaded heat-ODE system with time-dependent coefficient is discussed by choosing suitable backstepping transformation transferring the original heat-ODE system into an exponentially stable object system. We prove the existence of time-dependent kernels in forward and invertible transformation via successive approximation method, which is the novelty of the paper, at the same time, the exponential stability of closed-loop system is proved.

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