Exponential Stabilization of a Heat-ODE System Cascaded at Two Intermediate Points

Qin Wang, Zhongcheng Zhou
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Abstract

This paper considers the exponential stability of a heat-ODE system cascaded at two intermediate points. A new backstepping transformation with three kernels is introduced. Firstly, by adopting a reversible backstepping transformation to design a stabilizing feedback control law, we prove that the existence of smooth kernel functions in the forward and inverse transformations. Then, the exponential stability of the closed-loop system is proved based on the stability of target system and the invertibility of backstepping transformation. Finally, we verify the compatibility between the known assumption for the special case and the controllability assumption of this paper.
两个中间点级联的热- ode系统的指数稳定性
本文研究了两个中间点级联的热- ode系统的指数稳定性。提出了一种新的三核反演变换。首先,采用可逆反步变换设计稳定反馈控制律,证明了正、逆变换中光滑核函数的存在性;然后,基于目标系统的稳定性和反演变换的可逆性,证明了闭环系统的指数稳定性。最后,验证了已知的特殊情况假设与本文的可控性假设的相容性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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