An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems

DOI10.1051/COCV/2016038zbMath1353.49036OpenAlexW2409963356MaRDI QIDQ2835358

Antoine Girard, Pierre-Olivier Lamare, Christophe Prieur

Publication date: 2 December 2016

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/cocv/2016038

zbMATH Keywords

stabilityLyapunov methodoptimisationcontroller synthesishyperbolic PDE

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Feedback control (93B52) Dynamical systems in control (37N35) Existence theories for optimal control problems involving partial differential equations (49J20) First-order hyperbolic equations (35L02)

Related Items (6)

Regional stability and stabilization of a class of linear hyperbolic systems with nonlinear quadratic dynamic boundary conditions ⋮ Boundary control design for conservation laws in the presence of measurement disturbances ⋮ A partial integral equation (PIE) representation of coupled linear PDEs and scalable stability analysis using LMIs ⋮ Saturated boundary feedback control of quasi-linear hyperbolic balance laws with application to LWR traffic flow stabilization ⋮ Boundary observer-based control for hyperbolic PDE-ODE cascade systems with stochastic jumps ⋮ Supervisory switching control for linear hyperbolic systems

Uses Software

• YALMIP

Cites Work

• Stability and boundary stabilization of 1-D hyperbolic systems
• 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 LMI approach to \({\mathcal H}_\infty\) boundary control of semilinear parabolic and hyperbolic systems
• Nonlinear control of a coupled PDE/ODE system modeling a switched power converter with a transmission line
• Boundary observers for linear and quasi-linear hyperbolic systems with application to flow control
• Stability of Switched Linear Hyperbolic Systems by Lyapunov Techniques
• Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems
• Linear Matrix Inequalities in System and Control Theory
• Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems
• A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws
• Stabilization of a System of <formula formulatype="inline"> <tex Notation="TeX">$n+1$</tex></formula> Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input
• On the relation of delay equations to first-order hyperbolic partial differential equations
• Solving Hyperbolic PDEs in MATLAB

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