Smoothing Lyapunov functions

DOI10.1090/tran/7329zbMath1410.37025OpenAlexW2752199474MaRDI QIDQ4644945

Albert Fathi, Pierre Pageault

Publication date: 9 January 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/tran/7329

zbMATH Keywords

Lyapunov functionchain recurrence

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Lyapunov and storage functions (93D30) Generic properties, structural stability of dynamical systems (37C20) Stability theory for smooth dynamical systems (37C75)

Related Items (13)

Obstructions to Asymptotic Stabilization ⋮ On the existence of smooth Lyapunov functions for arbitrary closed sets ⋮ Smooth complete Lyapunov functions for ODEs ⋮ Flux in tilted potential systems: negative resistance and persistence ⋮ Extinction scenarios in evolutionary processes: a multinomial Wright-Fisher approach ⋮ Introducing some classes of stable systems without any smooth Lyapunov functions ⋮ Smooth complete Lyapunov functions for multifunctions ⋮ Existence of Lipschitz continuous Lyapunov functions strict outside the strong chain recurrent set ⋮ Computing complete Lyapunov functions for discrete-time dynamical systems ⋮ Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits ⋮ Existence of complete Lyapunov functions with prescribed orbital derivative ⋮ Minimization with differential inequality constraints applied to complete Lyapunov functions ⋮ Necessary conditions for feedback stabilization and safety

Cites Work

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• Conley barriers and their applications: Chain-recurrence and Lyapunov functions
• Shrinking cell-like decompositions of manifolds. Codimension three
• Chain recurrence, semiflows, and gradients
• On smooth time functions
• On the inversion of Ljapunov's second theorem on stability of motion
• The equivalence of close piecewise linear embeddings
• The gradient structure of a flow: I
• Lyapunov functions and attractors in arbitrary metric spaces
• Partitions of Unity for Countable Covers
• Aubry–Mather theory for homeomorphisms
• A metric approach to the converse Lyapunov theorem for continuous multivalued dynamics
• Smoothing Derivatives of Functions and Applications

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