Feedback stabilization of quasilinear hyperbolic systems with varying delays

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 PL

URI: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6347931&isnumber=6347808

DOI: 10.1109/MMAR.2012.6347931

Abstract

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.

Authors with CRIS profile

Markus Dick Lehrstuhl für Angewandte Mathematik Martin Gugat Lehrstuhl für Angewandte Mathematik Günter Leugering Lehrstuhl für Angewandte Mathematik

How to cite

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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