Numerical discretization of boundary control problems for systems of balance laws: Feedback stabilization. (May 2017)

• Record Type: Journal Article
• Authors: Göttlich, Simone; Schillen, Peter
• Is Part Of: European journal of control. Volume 35(2017:May)
• Page Start: 11
• Page End: 18
• Publication Date: 2017-05
• Subjects: Systems of balance laws -- Lyapunov function -- Feedback stabilization; 65Mxx -- 93D05 -- 65M08 -- 35L65; Control theory -- Periodicals; Automatic control -- Periodicals; Automatic control -- Mathematics -- Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.ejcon.2017.02.002
• Languages: English
• ISSNs: 0947-3580

Abstract

Abstract: We consider the boundary control of discretized problems based on systems of linear conservation laws including source terms. For a discrete Lyapunov function we prove the exponential decay in L 2 -norm using first-order finite volume methods. We give explicit computations of the decay rates and apply the proposed framework to the numerical boundary feedback stabilization of electric transmission lines given by the telegraphers equation.