Computation of local ISS Lyapunov functions with low gains via linear programming

DOI10.3934/dcdsb.2015.20.2477zbMath1366.37146OpenAlexW2139374224MaRDI QIDQ258401

Fabian R. Wirth, Robert Baier, Huijuan Li, Lars Grüne, Sigurður Freyr Hafstein

Publication date: 10 March 2016

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2015.20.2477

zbMATH Keywords

linear programmingLyapunov functionnonlinear systemlocal input-to-state stability

Mathematics Subject Classification ID

Applications of mathematical programming (90C90) Linear programming (90C05) Lyapunov and storage functions (93D30) Input-output approaches in control theory (93D25) Robust stability (93D09) Approximation methods and numerical treatment of dynamical systems (37M99)

Related Items (6)

What is the most suitable Lyapunov function? ⋮ Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions ⋮ Computation of non-monotonic Lyapunov functions for continuous-time systems ⋮ Sliding modes and Lyapunov functions for differential inclusions by linear programming ⋮ Computation of local ISS Lyapunov functions for discrete-time systems via linear programming ⋮ Review on computational methods for Lyapunov functions

Cites Work

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• Existence of piecewise linear Lyapunov functions in arbitrary dimensions
• On characterizations of the input-to-state stability property
• Linear programming based Lyapunov function computation for differential inclusions
• Stability analysis of complex dynamical systems. Some computational methods
• A constructive converse Lyapunov theorem on exponential stability
• A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems
• An ISS small gain theorem for general networks
• A regularization of Zubov’s equation for robust domains of attraction
• Small Gain Theorems for Large Scale Systems and Construction of ISS Lyapunov Functions
• Lyapunov function construction for ordinary differential equations with linear programming
• Further facts about input to state stabilization
• Numerical determination of domains of attraction for electrical power systems using the method of Zubov
• New characterizations of input-to-state stability
• Smooth stabilization implies coprime factorization
• A unified approach to controller design for achieving ISS and related properties
• A constructive converse Lyapunov theorem on asymptotic stability for nonlinear autonomous ordinary differential equations

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