Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10398791 | Automatica | 2011 | 6 Pages |
Abstract
The paper relates set-valued Lyapunov functions to pointwise asymptotic stability in systems described by a difference inclusion. Pointwise asymptotic stability of a set is a property which requires that each point of the set be Lyapunov stable and that every solution to the inclusion, from a neighborhood of the set, be convergent and have the limit in the set. Weak set-valued Lyapunov functions are shown, via an argument resembling an invariance principle, to imply this property. Strict set-valued Lyapunov functions are shown, in the spirit of converse Lyapunov results, to always exist for closed sets that are pointwise asymptotically stable.
Related Topics
Physical Sciences and Engineering
Engineering
Control and Systems Engineering
Authors
Rafal Goebel,