Boundary Stabilization with restricted observability

arXiv (Cornell University)

Abstract

Lyapunov functions are popularly used to investigate the stabilization problem of systems of hyperbolic conservation laws with boundary controls. In real life applications often not every boundary value can be observed. In this work, we show the stabilization under a restricted boundary observability. Thereby, we apply the boundary control directly on the observed (physical) variables. Using well-known stabilization results from the literature, we also discuss examples such as a density flow model or the Saint-Venant equations. This shows that a restricted observation can result in more restrictive control choices or can prevent the system from stabilizing.

Authors 3

1. Mapundi K. Banda

   University of Pretoria

   Affiliation as printed

   Department of Mathematics and Applied Mathematics , University of Pretoria , Private Bag X20 , Hatfield 0028 , Republic of South Africa ,

2. Jan O. Friedrich Aachen Chair of Numerical Analysis Institute for Geometry and Applied Mathematics

   RWTH Aachen University

   Affiliation as printed

   Chair of Numerical Analysis , Institute for Geometry and Applied Mathematics , RWTH Aachen University , Templer- graben 55 , 52056 Aachen , Germany

3. Michaël Herty Aachen Chair of Numerical Analysis Institute for Geometry and Applied Mathematics

   RWTH Aachen University

   Affiliation as printed

   Chair of Numerical Analysis , Institute for Geometry and Applied Mathematics , RWTH Aachen University , Templer- graben 55 , 52056 Aachen , Germany