ISS-based robustness to various neglected damping mechanisms for the 1-D wave PDE

DOI10.1007/s00498-023-00353-6zbMath1526.93211arXiv2112.11287OpenAlexW4365813923MaRDI QIDQ6073863

Publication date: 12 October 2023

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.11287

zbMATH Keywords

wave equation feedback stabilization input-to-state stability PDEs ISS Lyapunov functional thermoelasticity models

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Stabilization of systems by feedback (93D15) Input-output approaches in control theory (93D25) Wave equation (35L05)

Cites Work

Unnamed Item
Unnamed Item
The stability for a one-dimensional wave equation with nonlinear uncertainty on the boundary
Output-feedback adaptive control of a wave PDE with boundary anti-damping
Exponential stability of an elastic string with local Kelvin-Voigt damping
Stability results for the wave equation with indefinite damping
Input-to-state stability for PDEs
Functional analysis, Sobolev spaces and partial differential equations
Semigroups of linear operators and applications to partial differential equations
A direct method for the boundary stabilization of the wave equation
Controllability and stability of a second-order hyperbolic system with collocated sensor/actuator
Global exponential stability and input-to-state stability of semilinear hyperbolic systems for the \(L^2\) norm
Boundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundary
Compensating PDE actuator and sensor dynamics using Sylvester equation
Compensation of Wave Actuator Dynamics for Nonlinear Systems
Boundary Stabilization of a 1-D Wave Equation with In-Domain Antidamping
One-dimensional wave equation with set-valued boundary damping: well-posedness, asymptotic stability, and decay rates
Boundary Control of PDEs
Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks
A decreasing property of solutions of parabolic equations with applications to thermoelasticity
An Example on the Effect of Time Delays in Boundary Feedback Stabilization of Wave Equations
Not All Feedback Stabilized Hyperbolic Systems are Robust with Respect to Small Time Delays in Their Feedbacks
Extensions of a property of the heat equation to linear thermoelasticity and other theories
Spectrum and Stability for Elastic Systems with Global or Local Kelvin--Voigt Damping
Delay-Robust Control Design for Two Heterodirectional Linear Coupled Hyperbolic PDEs
Mathematical Modeling in Continuum Mechanics
Smooth stabilization implies coprime factorization
On the stabilization and stability robustness against small delays of some damped wave equations
Weak Input to State Estimates for 2D Damped Wave Equations with Localized and Nonlinear Damping
Input-to-State Stability of a Clamped-Free Damped String in the Presence of Distributed and Boundary Disturbances
Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions
Boundary-to-Displacement asymptotic gains for wave systems with Kelvin–Voigt damping
The Stabilization of a One-Dimensional Wave Equation by Boundary Feedback With Noncollocated Observation

This page was built for publication: ISS-based robustness to various neglected damping mechanisms for the 1-D wave PDE