Brief paper: Arbitrary decay rate for two connected strings with joint anti-damping by boundary output feedback

Authors:
Bao-Zhu Guo;Feng-Fei Jin
Affiliations:
Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, PR China and School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050 ...;Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, PR China
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

In this paper, we are concerned with the boundary stabilization of two connected strings with middle joint anti-damping for which all eigenvalues of the (control) free system are located on the right complex plane. We first design an explicit state feedback controller to achieve exponential stability for the closed-loop system. Consequently, we design the output feedback by using infinite-dimensional observer. The backstepping approach is adopted in investigation. It is shown that by using one boundary stabilizer only, the output feedback can make the closed-loop system exponentially stable with arbitrary decay rate.