Monotonicity Methods for Input-to-State Stability of Nonlinear Parabolic PDEs with Boundary Disturbances

DOI10.1137/17M1161877zbMath1406.93298arXiv1706.07224OpenAlexW2962806586WikidataQ114074309 ScholiaQ114074309MaRDI QIDQ4619479

Iasson Karafyllis, Andrii Mironchenko, Krstić, Miroslav

Publication date: 6 February 2019

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.07224

zbMATH Keywords

boundary controlnonlinear systemsparabolic systemsinfinite-dimensional systemsinput-to-state stabilitymonotone systems

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Nonlinear systems in control theory (93C10) Lyapunov and storage functions (93D30) Input-output approaches in control theory (93D25) Control/observation systems in abstract spaces (93C25) Semilinear parabolic equations (35K58)

Related Items (32)

Stability conditions for impulsive dynamical systems ⋮ ISS-like estimates for nonlinear parabolic PDEs with variable coefficients on higher dimensional domains ⋮ Integral input-to-state stability of unbounded bilinear control systems ⋮ Asymptotic gain results for attractors of semilinear systems ⋮ Approximations of Lyapunov functionals for ISS analysis of a class of higher dimensional nonlinear parabolic PDEs ⋮ Input-to-state stability of homogeneous infinite dimensional systems with locally Lipschitz nonlinearities ⋮ Robust Stability of a Nonlinear ODE-PDE System ⋮ Growth conditions for global exponential stability and exp-ISS of time-delay systems under point-wise dissipation ⋮ Input-to-state stability analysis of heat equation with boundary finite-time control ⋮ Exponential stabilization of the semilinear heat equation with nonlocal boundary conditions ⋮ Exponential input-to-state stability of delay Korteweg-de Vries-Burgers equations ⋮ Infinite-Dimensional Lur'e Systems: Input-To-State Stability and Convergence Properties ⋮ Monotonicity Methods for Input-to-State Stability of Nonlinear Parabolic PDEs with Boundary Disturbances ⋮ Input-to-State Stability for a Class of One-Dimensional Nonlinear Parabolic PDEs with Nonlinear Boundary Conditions ⋮ A local input-to-state stability result w.r.t. attractors of nonlinear reaction-diffusion equations ⋮ Noncoercive Lyapunov Functions for Input-to-State Stability of Infinite-Dimensional Systems ⋮ Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions ⋮ Input-to-state stabilization of an ODE-wave system with disturbances ⋮ Exponential input-to-state stabilization of a class of diagonal boundary control systems with delay boundary control ⋮ Input-to-state stability in sup norms for hyperbolic systems with boundary disturbances ⋮ Input-to-state stability of impulsive stochastic infinite dimensional systems with Poisson jumps ⋮ ISS property with respect to boundary disturbances for a class of Riesz-spectral boundary control systems ⋮ Stability and convergence properties of forced infinite-dimensional discrete-time Lur'e systems ⋮ Input-to-state stability of infinite-dimensional stochastic nonlinear systems ⋮ Stabilization of port-Hamiltonian systems by nonlinear boundary control in the presence of disturbances ⋮ ISS estimates in the spatial sup-norm for nonlinear 1-D parabolic PDEs ⋮ A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances ⋮ Robustness of global attractors: abstract framework and application to dissipative wave equations ⋮ Weak input-to-state stability: characterizations and counterexamples ⋮ Stochastic Input-to-State Stability of Impulsive Stochastic Nonlinear Systems in Infinite Dimensions ⋮ Dwell-time stability conditions for infinite dimensional impulsive systems ⋮ Input-to-state stability and integral input-to-state stability of non-autonomous infinite-dimensional systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Dissipation inequalities for the analysis of a class of PDEs
• ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws
• Strict Lyapunov functions for semilinear parabolic partial differential equations
• A Lyapunov--Krasovskii methodology for ISS and iISS of time-delay systems
• Local input-to-state stability: characterizations and counterexamples
• On the Lyapunov-Krasovskii methodology for the ISS of systems described by coupled delay differential and difference equations
• Semigroups of linear operators and applications to partial differential equations
• Adaptive nonlinear control without overparametrization
• On the stabilizability problem in Banach space
• Robust stabilization of delayed neural fields with partial measurement and actuation
• 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
• Small-gain theorem for ISS systems and applications
• Stabilization in spite of matched unmodeled dynamics and equivalent definition of input-to-state stability
• Controllability of switched differential-algebraic equations
• Input-to-state stability of infinite-dimensional control systems
• Infinite-dimensional feedback systems: the circle criterion and input-to-state stability
• On the ISS properties of a class of parabolic DPS' with discontinuous control using sampled-in-space sensing and actuation
• Lyapunov tools for predictor feedbacks for delay systems: inverse optimality and robustness to delay mismatch
• An ISS small gain theorem for general networks
• ISS with Respect to Boundary Disturbances for 1-D Parabolic PDEs
• A vector small-gain theorem for general non-linear control systems
• Construction of Lyapunov Functions for Interconnected Parabolic Systems: An iISS Approach
• Boundary Control of PDEs
• Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
• Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem
• Infinite-Dimensional Input-to-State Stability and Orlicz Spaces
• Monotonicity Methods for Input-to-State Stability of Nonlinear Parabolic PDEs with Boundary Disturbances
• Notions of exponential robust stochastic stability, ISS and their Lyapunov characterizations
• ISS In Different Norms For 1-D Parabolic Pdes With Boundary Disturbances
• Monotone control systems
• Closed-Form Boundary State Feedbacks for a Class of 1-D Partial Integro-Differential Equations
• Characterizations of input-to-state stability for infinite-dimensional systems
• Robust nonlinear control design. State-space and Lyapunov techniques
• Nonlinear observers: A circle criterion design and robustness analysis

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