Smoothing Lyapunov functions
Copyright policy )Smoothing Lyapunov functions
Since \textit{C. Conley}'s work [Ergodic Theory Dyn. Syst. 8, 11--26 (1988; Zbl 0687.58033); Isolated invariant sets and the Morse index. Providence, RI: American Mathematical Society (AMS) (1978; Zbl 0397.34056)], which showed the strong relation between Lyapunov functions and chain-recurrence, Lyapunov functions are also used to study general dynamical systems. In this work, the authors address the problem of smoothing Lyapunov functions for flows. They give a criterion for the approximation of a Lyapunov function by a smooth one.
- Georgia Institute of Technology United States
Lyapunov function, Lyapunov and storage functions, Stability of topological dynamical systems, Generic properties, structural stability of dynamical systems, Stability theory for smooth dynamical systems, chain recurrence
Lyapunov function, Lyapunov and storage functions, Stability of topological dynamical systems, Generic properties, structural stability of dynamical systems, Stability theory for smooth dynamical systems, chain recurrence
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