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Computational methods for Lyapunov functions

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  • Lyapunov functions, introduced by Lyapunov more than 100 years ago, are to this day one of the most important tools in the stability analysis of dynamical systems. They are functions which decrease along solution trajectories of systems, and they can be used to show stability of an invariant set, such as an equilibrium, as well as to determine its basin of attraction. Lyapunov functions have been considered for a variety of dynamical systems, such as continuous-times, discrete-time, linear, non-linear, non-smooth, switched, etc. Lyapunov functions are used and studied in different communities, such as Mathematics, Informatics and Engineering, often using different notations and methods.

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