Tikhonov theorem for linear hyperbolic systems

DOI10.1016/j.automatica.2015.03.028zbMath1330.93127OpenAlexW2057432879MaRDI QIDQ895105

Ying Tang, Christophe Prieur, Antoine Girard

Publication date: 26 November 2015

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2015.03.028

zbMATH Keywords

Lyapunov functionsingular perturbationTikhonov theoremlinear hyperbolic system

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Stabilization of systems by feedback (93D15) Application models in control theory (93C95) Perturbations in control/observation systems (93C73) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Time-scale analysis and singular perturbations in control/observation systems (93C70)

Related Items (8)

Regional stability and stabilization of a class of linear hyperbolic systems with nonlinear quadratic dynamic boundary conditions ⋮ Boundary feedback control of linear hyperbolic systems: application to the Saint-Venant-Exner equations ⋮ Design of adaptive output feedback synchronizing controllers for networked PDEs with boundary and in-domain structured perturbations and disturbances ⋮ Boundary control design for conservation laws in the presence of measurement disturbances ⋮ Stability analysis of coupled linear ODE-hyperbolic PDE systems with two time scales ⋮ Finite-time sliding mode control for singularly perturbed PDE systems ⋮ Singular Perturbation Approach for Linear Coupled ODE-PDE Systems ⋮ Singular perturbation approximation by means of a \(H^2\) Lyapunov function for linear hyperbolic systems

Cites Work

• Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws
• Two-step Lax-Friedrichs method
• Singular perturbation methods for slow-fast dynamics
• Asymptotic stability of a class of non-linear singularly perturbed systems
• Introduction to functional differential equations
• Singularly perturbed problems in partial differential equations: A survey
• Quadratic-type Lyapunov functions for singularly perturbed systems
• Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems
• Uniform asymptotic stability of non-linear singularly perturbed general and large-scale systems
• A two-stage Lyapunov-Bellman feedback design of a class of nonlinear systems
• Finite-Time Stabilization of $2\times2$ Hyperbolic Systems on Tree-Shaped Networks
• Solving Hyperbolic PDEs in MATLAB
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