Zhen, Zhiyuan; Tang, Shu-Xia; Zhou, Zhongcheng Stabilization of a heat-ODE system cascaded at a boundary point and an intermediate point. (English) Zbl 1386.93262 Asian J. Control 19, No. 5, 1834-1843 (2017). Summary: This paper considers the stabilization of a heat-ODE system cascaded at a boundary point and an intermediate point. The stabilizing feedback control law is designed by the backstepping method. Based on a novel transformation, we prove that all the kernel functions in the forward and inverse transformations are of the class \(C^2\). Moreover, the effectiveness of controller design is shown with a numerical simulation. Finally, we show the coherence between the controllability assumption of the main theorem in this paper and the known one for a special case with \(\lambda=0\). Cited in 3 Documents MSC: 93D21 Adaptive or robust stabilization 93D20 Asymptotic stability in control theory 93C20 Control/observation systems governed by partial differential equations 93C15 Control/observation systems governed by ordinary differential equations 35K10 Second-order parabolic equations Keywords:cascaded heat-ODE; backstepping; stabilization; intermediate point PDFBibTeX XMLCite \textit{Z. Zhen} et al., Asian J. Control 19, No. 5, 1834--1843 (2017; Zbl 1386.93262) Full Text: DOI