Review on computational methods for Lyapunov functions

Giesl, Peter and Hafstein, Sigurdur (2015) Review on computational methods for Lyapunov functions. Discrete and Continuous Dynamical Systems - Series B, 20 (8). pp. 2291-2331. ISSN 1531-3492

[img] PDF - Accepted Version
Download (755kB)

Abstract

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them.
Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ different methods such as series expan- sion, linear programming, linear matrix inequalities, collocation methods, al- gebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function.

Item Type: Article
Keywords: Lyapunov function, stability, basin of attraction, dynamical system, contraction metric, converse theorem, numerical method.
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Peter Giesl
Date Deposited: 05 Oct 2015 08:53
Last Modified: 06 Mar 2017 13:08
URI: http://sro.sussex.ac.uk/id/eprint/56983

View download statistics for this item

📧 Request an update