ISS-like estimates for nonlinear parabolic PDEs with variable coefficients on higher dimensional domains

DOI10.1016/j.sysconle.2020.104808zbMath1454.93246OpenAlexW3093804194WikidataQ114129647 ScholiaQ114129647MaRDI QIDQ826812

Jun Zheng, Guchuan Zhu

Publication date: 6 January 2021

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

Full work available at URL: https://doi.org/10.1016/j.sysconle.2020.104808

zbMATH Keywords

input-to-state stabilityweak maximum principlenonlinear parabolic PDEsboundary disturbance

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Nonlinear parabolic equations (35K55) Input-output approaches in control theory (93D25)

Related Items

Input-to-state stability analysis of heat equation with boundary finite-time control ⋮ ISS estimates in the spatial sup-norm for nonlinear 1-D parabolic PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Sampled-data boundary feedback control of 1-D parabolic PDEs
• A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances
• Input-to-state stability with respect to boundary disturbances for a class of semi-linear parabolic equations
• On continuity of solutions for parabolic control systems and input-to-state stability
• ISS property with respect to boundary disturbances for a class of Riesz-spectral boundary control systems
• ISS with Respect to Boundary Disturbances for 1-D Parabolic PDEs
• Infinite-Dimensional Input-to-State Stability and Orlicz Spaces
• Monotonicity Methods for Input-to-State Stability of Nonlinear Parabolic PDEs with Boundary Disturbances
• Approximate controllability of the semilinear heat equation
• Input-to-State Stability of a Clamped-Free Damped String in the Presence of Distributed and Boundary Disturbances
• Input-to-State Stability for a Class of One-Dimensional Nonlinear Parabolic PDEs with Nonlinear Boundary Conditions
• Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions
• A De Giorgi Iteration-Based Approach for the Establishment of ISS Properties for Burgers’ Equation With Boundary and In-domain Disturbances
• ISS In Different Norms For 1-D Parabolic Pdes With Boundary Disturbances
• On the relation of delay equations to first-order hyperbolic partial differential equations