Hirsch-Dick M, Gugat M, Leugering G (2012)
Publication Type: Conference contribution
Publication year: 2012
Edited Volumes: 2012 17th International Conference on Methods and Models in Automation and Robotics, MMAR 2012
Series: IEEEXplore
Pages Range: 125-130
Conference Proceedings Title: Methods and Models in Automation and Robotics (MMAR)
Event location: Miedzyzdroje, Poland
URI: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6347931&isnumber=6347808
DOI: 10.1109/MMAR.2012.6347931
We consider the feedback stabilization of quasilinear hyperbolic systems on star-shaped networks. We present boundary feedback controls with varying delays. The delays are given by C1-functions with bounded derivatives. We obtain the existence of unique C1-solutions on a given finite time interval. In order to measure the system evolution, we introduce an L2-Lyapunov function with delay terms. The feedback controls yield the exponential decay of the Lyapunov function with time. This implies the exponential stability of the system. Our results can be applied on the stabilization of the isothermal Euler equations with friction that model the gas flow in pipe networks. © 2012 IEEE.
APA:
Hirsch-Dick, M., Gugat, M., & Leugering, G. (2012). Feedback stabilization of quasilinear hyperbolic systems with varying delays. In Methods and Models in Automation and Robotics (MMAR) (pp. 125-130). Miedzyzdroje, Poland, PL.
MLA:
Hirsch-Dick, Markus, Martin Gugat, and Günter Leugering. "Feedback stabilization of quasilinear hyperbolic systems with varying delays." Proceedings of the 17th International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland 2012. 125-130.
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