Abstract
We consider stability of an infinite dimensional switching system, posed as a system of linear hyperbolic partial differential equations (PDEs) with reflecting boundaries, where the system parameters and the boundary conditions switch in time. Asymptotic stability of the solution for arbitrary switching is proved under commutativity of the advective velocity matrices and a joint spectral radius condition involving the boundary data.
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References
Frid, H.: Initial-boundary value problems for conservation laws. Journal of Differential Equations 128, 1–45 (1996)
Leugering, G., Schmidt, J.P.G.: On the modeling and stabilisation of flows in networks of open canals. SIAM Journal of Control and Optimization 41(1), 164–180 (2002)
Liberzon, D.: Switching in Systems and Control. In series Systems and Control: Foundations and Applications. Birkhauser (2003)
Li, T.-T.: Global classical solutions for quasilinear hyperbolic systems. In: Research in Applied Mathematics, Masson and Wiley, Paris, Milan, Barcelona (1994)
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Amin, S., Hante, F.M., Bayen, A.M. (2008). On Stability of Switched Linear Hyperbolic Conservation Laws with Reflecting Boundaries. In: Egerstedt, M., Mishra, B. (eds) Hybrid Systems: Computation and Control. HSCC 2008. Lecture Notes in Computer Science, vol 4981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78929-1_44
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DOI: https://doi.org/10.1007/978-3-540-78929-1_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78928-4
Online ISBN: 978-3-540-78929-1
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