Title :
Strong Stability of an Unstable Wave Equation by Boundary Feedback With Only Displacement Observation
Author :
Guo, Wei ; Shao, Zhi-Chao
Author_Institution :
Sch. of Inf. Technol. & Manage., Univ. of Int. Bus. & Econ., Beijing, China
Abstract :
The stabilization of a 1-D wave equation that contains instability at its free end and control at the other end is considered. The controller is designed through the estimated state that is designed in the case that only displacement is available. The method of “backstepping” is adopted in investigation. The C0 -semigroup theory and Lyapunov method are used to show that the closed-loop system is asymptotically stable.
Keywords :
Lyapunov methods; asymptotic stability; closed loop systems; feedback; group theory; state estimation; wave equations; 1D wave equation; C0-semigroup theory; Lyapunov method; asymptotic stability; backstepping method; boundary feedback; closed loop system; displacement observation; state estimation; unstable wave equation stability; Asymptotic stability; Backstepping; Displacement measurement; Eigenvalues and eigenfunctions; Equations; Observers; Propagation; Backstepping; boundary control; distributed parameter system; vibrating string;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2012.2204837
