A conceptual introduction to contraction theory

Abstract

The Contraction Theory is a relatively new methodology used to study of the stability of nonlinear dynamical systems. Because of its relative mathematical complexity, this theory could be a difficult thing to understand, especially for students and professionals not involved in the field of the differential geometry and nonlinear control theory. In order to make the Contraction Theory easier to introduce, this paper presents a simplified discussion of the motivational elements which give rise to the theory. Thus, it is intended the reader gains a solid understanding of nature of the contraction as well as the incremental stability, so as to he/she gets a suitable introduction to the subject and he/she can properly apply it into related subsequent studies.