TY - JOUR
T1 - State and output feedback boundary control for a coupled PDEODE 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 and National Nature Science Foundation under Grant 11026111 .
PY - 2011/8
Y1 - 2011/8
N2 - This note is devoted to stabilizing a coupled PDEODE system with interaction at the interface. First, a state feedback boundary controller is designed, and the system is transformed into an exponentially stable PDEODE cascade with an invertible integral transformation, where PDE backstepping is employed. Moreover, the solution to the resulting closed-loop system is derived explicitly. Second, an observer is proposed, which is proved to exhibit good performance in estimating the original coupled system, and then an output feedback boundary controller is obtained. 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 provided. The boundary controller and observer for a scalar coupled PDEODE system as well as the solutions to the closed-loop systems are given explicitly.
AB - This note is devoted to stabilizing a coupled PDEODE system with interaction at the interface. First, a state feedback boundary controller is designed, and the system is transformed into an exponentially stable PDEODE cascade with an invertible integral transformation, where PDE backstepping is employed. Moreover, the solution to the resulting closed-loop system is derived explicitly. Second, an observer is proposed, which is proved to exhibit good performance in estimating the original coupled system, and then an output feedback boundary controller is obtained. 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 provided. The boundary controller and observer for a scalar coupled PDEODE system as well as the solutions to the closed-loop systems are given explicitly.
KW - Boundary control
KW - Coupled system
KW - Output feedback
KW - PDEs
UR - http://www.scopus.com/inward/record.url?scp=79959728879&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2011.04.011
DO - 10.1016/j.sysconle.2011.04.011
M3 - Article
AN - SCOPUS:79959728879
SN - 0167-6911
VL - 60
SP - 540
EP - 545
JO - Systems and Control Letters
JF - Systems and Control Letters
IS - 8
ER -