Title :
Exponential stability of a coupled Heat-ODE system
Author :
Dong-Xia Zhao ; Jun-Min Wang
Author_Institution :
Dept. of Math., Beijing Inst. of Technol., Beijing, China
Abstract :
This paper addresses the feedback stabilization of an interconnected Heat-ODE system with the Dirichlet interconnection. The “interconnection” between the heat equation and the ODE are bi-directional, in which the Dirichlet boundary observation of the heat equation is fed into the ODE, and the velocity of ODE is flowed into the boundary of the heat equation. The semigroup approach is adopted in investigation. By a detailed analysis, we obtain the asymptotic expressions of eigenvalues and eigenfunctions. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. This deduces the spectrum-determined growth condition for the C0-semigroup, and as a consequence, the exponential stability of the system is then followed. Numerical simulations are presented.
Keywords :
Hilbert spaces; asymptotic stability; differential equations; eigenvalues and eigenfunctions; feedback; group theory; heat systems; interconnected systems; state-space methods; C0-semigroup; Dirichlet boundary observation; Dirichlet interconnection; Hilbert state space; ODE velocity; Riesz basis; asymptotic eigenvalues-and-eigenfunctions expressions; bidirectional interconnection; coupled heat-ODE system; exponential stability; feedback stabilization; generalized eigenfunctions; heat equation boundary; interconnected heat-ODE system; numerical simulations; spectrum-determined growth condition; Control theory; Delays; Eigenvalues and eigenfunctions; Equations; Heating; Mathematical model; Stability; Dirichlet interconnection; Exponential stability; Heat equation; Riesz basis;
Conference_Titel :
Control and Decision Conference (CCDC), 2013 25th Chinese
Conference_Location :
Guiyang
Print_ISBN :
978-1-4673-5533-9
DOI :
10.1109/CCDC.2013.6560914
