Contraction theory is an analytical tool to study differential dynamics of a non-autonomous
(ie, time-varying) nonlinear system under a contraction metric defined with a uniformly …

In this chapter we present a state space interpretation of the small gain and passivity
approach of the previous chapter. Moreover, we will come to some kind of synthesis …

We introduce the concept of a control contraction metric, extending contraction analysis to
constructive nonlinear control design. We derive sufficient conditions for exponential …

Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic
systems stably coexist. We study global exponential synchronization and concurrent …

This paper introduces a methodology for differential nonlinear stability analysis using
contraction theory (Lohmiller and Slotine, 1998). The methodology includes four distinct …

This paper addresses the problem of providing mathematical conditions that allow one to
ensure that biological networks, such as transcriptional systems, can be globally entrained …

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 contraction properties of the extended Kalman filter, viewed as a deterministic observer
for nonlinear systems, are analyzed. The approach relies on the study of an auxiliary “virtual” …

This article presents ConVex optimization-based Stochastic steady-state Tracking Error
Minimization (CV-STEM), a new state feedback control framework for a class of Itô stochastic …

In this brief, the contraction theory is applied to the synchronization of a network. The
association between the contraction principle, the Lyapunov exponents of a system, and the …