TY - JOUR
T1 - Stabilization for a coupled PDE-ODE control system
AU - Tang, Shuxia
AU - Xie, Chengkang
N1 - Funding Information:
This work is supported by the Fundamental Research Funds for the Central Universities under contract XDJK2009C099 .
PY - 2011/10
Y1 - 2011/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80052596771&partnerID=8YFLogxK
U2 - 10.1016/j.jfranklin.2011.06.008
DO - 10.1016/j.jfranklin.2011.06.008
M3 - Article
AN - SCOPUS:80052596771
SN - 0016-0032
VL - 348
SP - 2142
EP - 2155
JO - Journal of the Franklin Institute
JF - Journal of the Franklin Institute
IS - 8
ER -