Nodal Stabilization of the Flow in a Network with a Cycle
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F. Alabau-Boussouira, V. Perrollaz, and L. Rosier, Finite-time stabilization of a network of strings, Mathematical Control and Related Fields, 5 (2015), 721–742.
F. Ancona and A. Marson, Asymptotic stabilization of systems of conservation laws by controls acting at a single boundary point, in Control methods in PDEdynamical systems. AMS-IMS-SIAM joint summer research conference, Snowbird, UT, USA, July 3–7, 2005, Providence, RI: American Mathematical Society (AMS), 2007, 1–43.
M. K. Banda, M. Herty, and A. Klar, Gas flow in pipeline networks, Networks & Heterogeneous Media, 1 (2006), 41–56.
C. Bardos, G. Lebeau, and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), 1024–1065.
G. Bastin and J.-M. Coron, Stability and boundary stabilization of 1-D hyperbolic systems, vol. 88, Basel: Birkh¨auser/Springer, 2016.
G. Bastin, J.-M. Coron, and B. d?Andr´ea-Novel, On Lyapunov stability of linearised Saint-Venant equations for a sloping channel, Netw. Heterog. Media, 4 (2009), 177–187.
R. M. Colombo and M. Garavello, On the Cauchy problem for the p- system at a junction, SIAM J. Math. Anal., 39 (2008), 1456–1471.
R. M. Colombo, M. Herty, and V. Sachers, On 2 2 conservation laws at a junction, SIAM J. Math. Anal., 40 (2008), 605–622.
C. M. Dafermos, Hyperbolic conservation laws in continuum physics, vol. 325 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, fourth ed., 2016.
S. Gerster, M. Bambach, M. Herty, and M. Imran, Feedback control for random, linear hyperbolic balance laws, International Journal for Uncertainty Quantification, 2021.
Q. Gu and T. Li, Exact boundary observability for quasilinear wave equations in a planar tree-like network of strings, Journal de Math ematiques Pures et Appliqu´ees, 95 (2011), 1–17.
M. Gugat, F. Hante, M. Hirsch-Dick, and G. Leugering, Stationary states in gas networks, Networks and Heterogeneous Media, 10 (2015), 295–320.
M. Gugat and M. Herty, Existence of classical solutions and feedback stabilization for the flow in gas networks, ESAIM Control Optim. Calc. Var., 17 (2011), 28–51.
M. Gugat and M. Herty, Limits of stabilizability for a semilinear model for gas pipeline flow, in Optimization and Control for Partial Differential Equations, De Gruyter, 2021, 1–13.
M. Gugat, M. Hirsch-Dick, and G. Leugering, Gas Flow in Fan-Shaped Networks: Classical Solutions and Feedback Stabilization, SIAM Journal on Control and Optimization, 49 (2011), 2101–2117.
M. Gugat and M. Tucsnak, An example for the switching delay feedback stabilization of an infinite dimensional system: The boundary stabilization of a string, Systems and Control Letters, 60 (2011), 226–230.
M. Gugat and S. Ulbrich, Lipschitz solutions of initial boundary value problems for balance laws, Mathematical Models and Methods in Applied Sciences, 28 (2018), 921– 951.
A. Hayat and P. Shang, Exponential stability of density-velocity systems with boundary conditions and source term for the H2-norm. Preprint, July 2019.
A. Hayat and P. Shang, A quadratic lyapunov function for saint-venant equations with arbitrary friction and space-varying slope, Automatica, 100 (2019), 52–60.
F. John, Partial differential equations. 4th ed., vol. 1, Springer, New York, NY, 1982.
J. E. Lagnese, G. Leugering, and E. J. P. G. Schmidt, Modeling, analysis and control of dynamic elastic multi-link structures, Boston, MA: Birkh? user, 1994.
G. Leugering and E. Zuazua, On exact controllability of generic trees, ESAIM: Proc., 8 (2000), 95–105.
T. Li, Controllability and observability for quasilinear hyperbolic systems, vol. 3 of AIMS Series on Applied Mathematics, American Institute of Mathematical Sciences (AIMS), Springfield, MO; Higher Education Press, Beijing, 2010.
M. Schmidt, D. Amann, R. Burlacu, J. Humpola, I. Joormann, N. Kanelakis, T. Koch, D. Oucherif, M. Pfetsch, L. Schewe, R. Schwarz, and M. Sirvent, Gaslib a library of gas network instances, Data, 2 (2017).
DOI: http://dx.doi.org/10.15421/1421O6
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