Methodological remarks on contraction theory
J Jouffroy, JJE Slotine - … 43rd IEEE Conference on Decision and …, 2004 - ieeexplore.ieee.org
Because contraction analysis stems from a differential and incremental framework, the
nature and methodology of contraction-based proofs are significantly different from those of …
nature and methodology of contraction-based proofs are significantly different from those of …
Some ancestors of contraction analysis
J Jouffroy - Proceedings of the 44th IEEE Conference on …, 2005 - ieeexplore.ieee.org
Contraction analysis is a recent tool for analyzing the convergence behavior of nonlinear
systems in state-space form (see Lohmiller and Slotine [16] for the main reference) …
systems in state-space form (see Lohmiller and Slotine [16] for the main reference) …
A simple extension of contraction theory to study incremental stability properties
J Jouffroy - 2003 European Control Conference (ECC), 2003 - ieeexplore.ieee.org
Contraction theory is a recent tool enabling to study the stability of nonlinear systems
trajectories with respect to one another, and therefore belongs to the class of incremental …
trajectories with respect to one another, and therefore belongs to the class of incremental …
Convergence properties for discrete-time nonlinear systems
Three similar convergence notions are considered. Two of them are the long established
notions of convergent dynamics and incremental stability. The other is the more recent …
notions of convergent dynamics and incremental stability. The other is the more recent …
A contraction theory-based analysis of the stability of the deterministic extended Kalman filter
S Bonnabel, JJ Slotine - IEEE Transactions on Automatic …, 2014 - ieeexplore.ieee.org
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” …
for nonlinear systems, are analyzed. The approach relies on the study of an auxiliary “virtual” …
Contraction methods for nonlinear systems: A brief introduction and some open problems
Z Aminzare, ED Sontagy - 53rd IEEE Conference on Decision …, 2014 - ieeexplore.ieee.org
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 …
dynamical systems. Under sometimes easy to check hypotheses, systems can be shown to …
A perspective on convergence of adaptive control algorithms
This paper presents an overview of the current status of convergence theory for adaptive
control algorithms. Rather than giving a comprehensive survey, the paper aims to …
control algorithms. Rather than giving a comprehensive survey, the paper aims to …
Control system design for mechanical systems using contraction theory
W Lohmiller, JJE Slotine - IEEE Transactions on Automatic …, 2000 - ieeexplore.ieee.org
Contraction theory is a control system tool based on an exact differential analysis of
convergence. After establishing new combination properties of contracting systems, the …
convergence. After establishing new combination properties of contracting systems, the …
Contraction theory on Riemannian manifolds
JW Simpson-Porco, F Bullo - Systems & Control Letters, 2014 - Elsevier
Contraction theory is a methodology for assessing the stability of trajectories of a dynamical
system with respect to one another. In this work, we present the fundamental results of …
system with respect to one another. In this work, we present the fundamental results of …
Contractive systems with inputs
ED Sontag - Perspectives in Mathematical System Theory, Control …, 2010 - Springer
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 …
external inputs. Under sometimes easy to check hypotheses, systems can be shown to have …