Dissipative Boundary Conditions for One-Dimensional Quasi-linear Hyperbolic Systems: Lyapunov Stability for the $C^1$-Norm

DOI10.1137/14097080XzbMath1316.35179OpenAlexW1869060484MaRDI QIDQ5254879

Georges Bastin, Jean-Michel Coron

Publication date: 10 June 2015

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/14097080x

zbMATH Keywords

exponential stability

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Lyapunov and storage functions (93D30) Asymptotic stability in control theory (93D20) First-order nonlinear hyperbolic equations (35L60) Initial-boundary value problems for second-order hyperbolic systems (35L53)

Related Items (32)

Neumann boundary feedback stabilization for a nonlinear wave equation: A strict \(H^2\)-Lyapunov function ⋮ Dissipative boundary conditions for \(2\times 2\) hyperbolic systems of conservation laws for entropy solutions in BV ⋮ Numerical feedback stabilization with applications to networks ⋮ High-gain observer for \(3 \times 3\) linear heterodirectional hyperbolic systems ⋮ Finite-time boundary stabilization of general linear hyperbolic balance laws via Fredholm backstepping transformation ⋮ Time-periodic solutions to quasilinear hyperbolic systems with time-periodic boundary conditions ⋮ Numerical boundary control for semilinear hyperbolic systems ⋮ On boundary stability of inhomogeneous 2 × 2 1-D hyperbolic systems for the C¹ norm ⋮ On L^∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control ⋮ Feedback stabilization for a coupled PDE-ODE production system ⋮ Saturated boundary feedback stabilization for LWR traffic flow model ⋮ Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems ⋮ Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions ⋮ Boundary Exponential Stabilization of 1-Dimensional Inhomogeneous Quasi-Linear Hyperbolic Systems ⋮ 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 ⋮ Optimal tracking control for a class of boundary controlled linear coupled hyperbolic PDE systems: application to plug flow reactor with temperature output feedback ⋮ Perturbations of superstable linear hyperbolic systems ⋮ Numerical discretization of boundary control problems for systems of balance laws: feedback stabilization ⋮ Input-to-state stability in sup norms for hyperbolic systems with boundary disturbances ⋮ Controllability and stabilization of a conservation law modeling a highly re-entrant manufacturing system ⋮ Discretized feedback control for systems of linearized hyperbolic balance laws ⋮ Feedback control of scalar conservation laws with application to density control in freeways by means of variable speed limits ⋮ Book review of: Iasson Karafyllis and Miroslav Krstic, Input-to-state stability for PDEs ⋮ Small-time global stabilization of the viscous Burgers equation with three scalar controls ⋮ On the finite-time stabilization of some hyperbolic control systems by boundary feedback laws: Lyapunov approach ⋮ Finite Time Stabilization of Nonautonomous First-Order Hyperbolic Systems ⋮ Boundary Stability of 1-D Nonlinear Inhomogeneous Hyperbolic Systems for the $C^{1}$ Norm ⋮ Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems ⋮ Contributions to the Problem of High-Gain Observer Design for Hyperbolic Systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws
• Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws
• On boundary feedback stabilization of non-uniform linear \(2\times 2\) hyperbolic systems over a bounded interval
• An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type
• Robust boundary control of systems of conservation laws
• Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions
• The effect of boundary damping for the quasilinear wave equation
• Global smooth solutions of dissipative boundary value problems for first order quasilinear hyperbolic systems
• Introduction to functional differential equations
• Boundary feedback control in networks of open channels.
• A Hamiltonian perspective to the stabilization of systems of two conservation laws
• Control of systems of conservation laws with boundary errors
• Boundary observers for linear and quasi-linear hyperbolic systems with application to flow control
• Boundary control of hyperbolic conservation laws using a frequency domain approach
• Stability of linear density-flow hyperbolic systems under PI boundary control
• A simple constructive proof of Kronecker's density theorem
• Output-feedback stabilization of an unstable wave equation
• Local Exponential $H^2$ Stabilization of a $2\times2$ Quasilinear Hyperbolic System Using Backstepping
• Boundary Stabilization of a 1-D Wave Equation with In-Domain Antidamping
• Existence of classical solutions and feedback stabilization for the flow in gas networks
• Gas Flow in Fan-Shaped Networks: Classical Solutions and Feedback Stabilization
• Boundary Control of PDEs
• Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method
• Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems
• Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions
• Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems
• On the Modelling and Stabilization of Flows in Networks of Open Canals
• A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws
• Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems
• Lyapunov-Based Boundary Control for A Class of Hyperbolic Lotka–Volterra Systems
• Disturbance rejection in 2 x 2 linear hyperbolic systems
• Finite-Time Stabilization of $2\times2$ Hyperbolic Systems on Tree-Shaped Networks

This page was built for publication: Dissipative Boundary Conditions for One-Dimensional Quasi-linear Hyperbolic Systems: Lyapunov Stability for the $C^1$-Norm