Finite-dimensional output stabilization for a class of linear distributed parameter systems -- a small-gain approach

DOI10.1016/j.sysconle.2022.105237zbMath1492.93150arXiv2104.06102OpenAlexW4225420884MaRDI QIDQ2670751

Thomas Meurer, Lars Grüne

Publication date: 1 June 2022

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

Full work available at URL: https://arxiv.org/abs/2104.06102

zbMATH Keywords

partial differential equationsspillovermodal approximationinput-to-output stabilitysmall-gain theorydiffusion-reaction systems

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Feedback control (93B52) Input-output approaches in control theory (93D25) Linear systems in control theory (93C05)

Related Items (5)

Output Feedback Stabilization of a Reaction-Diffusion PDE in the Presence of Saturations of the Input and Its Time Derivatives ⋮ Nonlinear boundary output feedback stabilization of reaction-diffusion equations ⋮ Boundary output feedback stabilization of state delayed reaction-diffusion PDEs ⋮ Boundary output feedback stabilisation of a class of reaction–diffusion PDEs with delayed boundary measurement ⋮ Output feedback stabilization of an ODE-reaction-diffusion PDE cascade with a long interconnection delay

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Eigenvalues and eigenvectors of semigroup generators obtained from diagonal generators by feedback
• The Galerkin method and feedback control of linear distributed parameter systems
• Pole assignment for distributed systems by finite-dimensional control
• Finite-dimensional control of distributed parameter systems by Galerkin approximation of infinite dimensional controllers
• Robust stabilization of infinite dimensional systems by finite dimensional controllers
• Finite-dimensional controllers for linear distributed parameter systems: Exponential stability using residual mode filters
• Active control of flexible systems
• Necessary conditions for exact controllability with a finite-dimensional input space
• A nonlinear small-gain theorem for large-scale infinite-dimensional systems
• Small-gain theorem for ISS systems and applications
• Constructive method for finite-dimensional observer-based control of 1-D parabolic PDEs
• Delayed finite-dimensional observer-based control of 1-D parabolic PDEs
• Numerical criterion for the stabilization of steady states of the Navier-Stokes equations
• Finite-dimensional observer-based control of linear distributed parameter systems using cascaded output observers
• A Direct Approach to Compensator Design for Distributed Parameter Systems
• Feedback Stabilization of Linear Diffusion Systems
• Admissible Input Elements for Systems in Hilbert Space and a Carleson Measure Criterion
• Controller design for distributed systems based on Hankel-norm approximations
• Finite-Dimensional Compensators for Infinite-Dimensional Systems with Unbounded Input Operators
• A note on spillover and robustness for flexible systems
• Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input
• Modal Control of Certain Flexible Dynamic Systems
• Feedback control of linear diffusion processes
• Global Steady-State Controllability of One-Dimensional Semilinear Heat Equations
• Feedback Stabilization of a 1-D Linear Reaction–Diffusion Equation With Delay Boundary Control
• Control of Wave and Beam PDEs

This page was built for publication: Finite-dimensional output stabilization for a class of linear distributed parameter systems -- a small-gain approach