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 …

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both
in theory and applications. They provide sufficient conditions for the stability of equilibria or …

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

Contraction theory provides an elegant way to analyze the behaviors of certain nonlinear
dynamical systems. Under sometimes easy to check hypotheses, systems can be shown to …

In this article, we study necessary and sufficient conditions for contraction and incremental
stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak …

We provide a novel robust stability analysis for moving horizon estimation (MHE) using a
Lyapunov function. In addition, we introduce linear matrix inequalities (LMIs) to verify the …

This tutorial paper provides an introduction to recently developed tools for machine learning,
especially learning dynamical systems (system identification), with stability and robustness …

Absolute stability attracted much attention in the 1960s. Several stability conditions for loops
with slope-restricted nonlinearities were developed. Results such as the Circle Criterion and …

The multiplicative and additive compounds of a matrix play an important role in geometry,
multilinear algebra, the asymptotic analysis of nonlinear dynamical systems, and in …

In this article, we propose a new approach to design globally convergent reduced-order
observers for nonlinear control systems via contraction analysis and convex optimization …