Discretized feedback control for systems of linearized hyperbolic balance laws

DOI10.3934/mcrf.2019024zbMath1429.37056OpenAlexW2939304377WikidataQ127980992 ScholiaQ127980992MaRDI QIDQ2280174

Stephan Gerster, Michael Herty

Publication date: 18 December 2019

Published in: Mathematical Control and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mcrf.2019024

zbMATH Keywords

Lyapunov functionfeedback stabilizationbalance lawsshallow water equationsisothermal Euler equations

Mathematics Subject Classification ID

Feedback control (93B52) Stabilization of systems by feedback (93D15) Perturbations in control/observation systems (93C73) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Linearizations (93B18) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Dynamical systems in control (37N35)

Related Items (5)

Exponential stability of a general slope limiter scheme for scalar conservation laws subject to a dissipative boundary condition ⋮ On the Stability of Robust Dynamical Low-Rank Approximations for Hyperbolic Problems ⋮ Numerical boundary control for semilinear hyperbolic systems ⋮ Turnpike properties of optimal boundary control problems with random linear hyperbolic systems ⋮ Input-to-state stability of non-uniform linear hyperbolic systems of balance laws via boundary feedback control

Cites Work

• Unnamed Item
• Stability and boundary stabilization of 1-D hyperbolic systems
• \(H^2\)-stabilization of the isothermal Euler equations: a Lyapunov function approach
• Gas flow in pipeline networks
• Lyapunov stability analysis of networks of scalar conservation laws
• Global boundary controllability of the Saint-Venant system for sloped canals with friction
• Boundary feedback control in networks of open channels.
• Global boundary controllability of the de St. Venant equations between steady states
• Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws
• Classical solutions and feedback stabilization for the gas flow in a sequence of pipes
• Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms
• Numerical discretization of boundary control problems for systems of balance laws: feedback stabilization
• On Lyapunov stability of linearised Saint-Venant equations for a sloping channel
• Global controllability between steady supercritical flows in channel networks
• Existence of classical solutions and feedback stabilization for the flow in gas networks
• Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems
• Positive diagonal solutions to the Lyapunov equations
• Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations
• On the Modelling and Stabilization of Flows in Networks of Open Canals
• Dissipative Boundary Conditions for One-Dimensional Quasi-linear Hyperbolic Systems: Lyapunov Stability for the $C^1$-Norm
• A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws

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