Stabilization for a coupled PDE-ODE control system

Shuxia Tang, Chengkang Xie

Research output: Contribution to journalArticlepeer-review

96 Scopus citations


A control system of an ODE and a diffusion PDE is discussed in this paper. The novelty lies in that the system is coupled. The method of PDE backstepping as well as some special skills is resorted in stabilizing the coupled PDEODE control system, which is transformed into an exponentially stable PDEODE cascade with an invertible integral transformation. And a state feedback boundary controller is designed. Moreover, an exponentially convergent observer for anti-collocated setup is proposed, and the output feedback boundary control problem is solved. For both the state and output feedback boundary controllers, exponential stability analyses in the sense of the corresponding norms for the resulting closed-loop systems are given through rigid proofs.

Original languageEnglish
Pages (from-to)2142-2155
Number of pages14
JournalJournal of the Franklin Institute
Issue number8
StatePublished - Oct 2011


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