Contractive systems with inputs

Abstract

Contraction theory provides an elegant way of analyzing the behaviors of systems subject to external inputs. Under sometimes easy to check hypotheses, systems can be shown to have the incremental stability property that all trajectories converge to a unique solution. This property is especially interesting when forcing functions are periodic (a globally attracting limit cycle results), as well as in the context of establishing synchronization results. The present paper provides a self-contained introduction to some basic results, with a focus on contractions with respect to non-Euclidean metrics. © 2010 Springer-Verlag Berlin Heidelberg.