On Contraction Analysis for Non-linear Systems

@article{Lohmiller1998OnCA,
  title={On Contraction Analysis for Non-linear Systems},
  author={Winfried Lohmiller and Jean-Jacques E. Slotine},
  journal={Autom.},
  year={1998},
  volume={34},
  pages={683-696}
}
On contraction analysis for hybrid systems
TLDR
This work generalizes infinitesimal contraction analysis to hybrid systems governed by interacting differential and difference equations.
Higher-Order Nonlinear Contraction Analysis
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem
Contraction analysis: a practical approach to nonlinear control applications
  • W. Lohmiller, J. Slotine
  • Mathematics
    Proceedings of the 1998 IEEE International Conference on Control Applications (Cat. No.98CH36104)
  • 1998
Contraction theory is a recently developed nonlinear analysis tool which may be viewed as an exact generalization of linear eigenvalues analysis. Based on a differential analysis of convergence, it
Contraction analysis of non-linear distributed systems
Contraction theory is a comparatively recent dynamic analysis and non-linear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory
Contraction methods for nonlinear systems: A brief introduction and some open problems
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 have the incremental
On infinitesimal contraction analysis for hybrid systems
TLDR
This work generalizes infinitesimal contraction analysis to hybrid systems governed by interacting differential and difference equations and leverages an intrinsic distance function to derive the first contraction results for hybrid systems without restrictions on mode sequence or dwell time.
Generalizing infinitesimal contraction analysis to hybrid systems
Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological,
Control system design for mechanical systems using contraction theory
TLDR
After establishing new combination properties of contracting systems, the paper derives new controller and observer designs for mechanical systems such as aircraft and underwater vehicles.
A Tutorial on Incremental Stability Analysis using Contraction Theory
TLDR
A methodology for dierential nonlinear stability analysis using contraction theory (Lohmiller and Slotine, 1998) is introduced and the approach is illustrated on several simple examples.
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