A quadratic Lyapunov function for hyperbolic density-velocity systems with nonuniform steady states

DOI10.1016/j.sysconle.2017.03.013zbMath1370.93193OpenAlexW2610839556MaRDI QIDQ2407248

Jean-Michel Coron, Georges Bastin

Publication date: 29 September 2017

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.sysconle.2017.03.013

zbMATH Keywords

stabilityLyapunov functionhyperbolic systemsEuler equationpartial differential equation

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Lyapunov and storage functions (93D30) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Asymptotic stability in control theory (93D20) First-order hyperbolic systems (35L40)

Related Items (11)

Networks of geometrically exact beams: well-posedness and stabilization ⋮ Stabilization of the linearized water tank system ⋮ Controller design for heterogeneous traffic with bottleneck and disturbances ⋮ On boundary stability of inhomogeneous 2 × 2 1-D hyperbolic systems for the C¹ norm ⋮ Feedforward boundary control of \(2\times 2\) nonlinear hyperbolic systems with application to Saint-Venant equations ⋮ Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation ⋮ A quadratic Lyapunov function for Saint-Venant equations with arbitrary friction and space-varying slope ⋮ Input-to-state stability of non-uniform linear hyperbolic systems of balance laws via boundary feedback control ⋮ Exponential stability of density-velocity systems with boundary conditions and source term for the \(H^2\) norm ⋮ Global exponential stability and input-to-state stability of semilinear hyperbolic systems for the \(L^2\) norm ⋮ PI controllers for the general Saint-Venant equations

Cites Work

• Stability and boundary stabilization of 1-D hyperbolic systems
• On boundary feedback stabilization of non-uniform linear \(2\times 2\) hyperbolic systems over a bounded interval
• \(H^2\)-stabilization of the isothermal Euler equations: a Lyapunov function approach
• Classical solutions and feedback stabilization for the gas flow in a sequence of pipes
• Local Exponential $H^2$ Stabilization of a $2\times2$ Quasilinear Hyperbolic System Using Backstepping
• Existence of classical solutions and feedback stabilization for the flow in gas networks
• Gas Flow in Fan-Shaped Networks: Classical Solutions and Feedback Stabilization
• Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems
• A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws

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