Abstract
SummaryThis paper considers the stabilization of a general linear heat‐ODE system coupling at an intermediate point which is an extension from our previous work on stabilizing a coupled system of a heat PDE and a second‐order ODE. A novel backstepping transformation is proposed which can overcome the difficulty of using the one proposed in our previous work to a more general system considered in the current paper. Existence of smooth kernels in both the forward and inverse transformations is proved. Also, we show that forward and inverse transformations are a mutually inverse pair governed by the kernels equations. Finally, the effectiveness of the controller design is demonstrated with some numerical examples for heat‐ODE systems. Copyright © 2017 John Wiley & Sons, Ltd.
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