On Three Generalizations of Contraction
Dynamical Systems
2014-06-06 v1
Abstract
We introduce three forms of generalized contraction (GC). Roughly speaking, these are motivated by allowing contraction to take place after small transients in time and/or amplitude. Indeed, contraction is usually used to prove asymptotic properties, like convergence to an attractor or entrainment to a periodic excitation, and allowing initial transients does not affect this asymptotic behavior. We provide sufficient conditions for GC, and demonstrate their usefulness using examples of systems that are not contractive, with respect to any norm, yet are GC.
Cite
@article{arxiv.1406.1474,
title = {On Three Generalizations of Contraction},
author = {Eduardo D. Sontag and Michael Margaliot and Tamir Tuller},
journal= {arXiv preprint arXiv:1406.1474},
year = {2014}
}