INTEGRATOR BACKSTEPPING USING CONTRACTION THEORY: A BRIEF METHODOLOGICAL NOTE.

@article{Jouffryo2002INTEGRATORBU,
  title={INTEGRATOR BACKSTEPPING USING CONTRACTION THEORY: A BRIEF METHODOLOGICAL NOTE.},
  author={J{\'e}r{\^o}me Jouffryo and Jacques Lottin},
  journal={IFAC Proceedings Volumes},
  year={2002},
  volume={35},
  pages={471-475}
}
Abstract While the use of Lyapunov function candidates for integrator backstepping has been extensively studied in the literature, little research has been conducted regarding the applicability of the so-called incremental stability approaches. This note addresses the problem of the use of an incremental approach, i.e. contraction theory to the integrator backstepping design on the methodological aspect. After briefly recalling basic results from contraction theory, a full contraction-based… 

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References

SHOWING 1-10 OF 13 REFERENCES

On Contraction Analysis for Non-linear Systems

A Lyapunov approach to incremental stability properties

  • D. Angeli
  • Mathematics
    IEEE Trans. Autom. Control.
  • 2002
The aim is to present a framework for understanding questions of incremental stability fully compatible with the well-known input-to-state stability approach.

Nonlinear output feedback control of dynamically positioned ships using vectorial observer backstepping

This paper proposes a globally exponentially stable (GES) nonlinear control where a nonlinear observer is included in the design such that only position measurements are required.

Nonlinear and adaptive control de-sign

Using a pedagogical style along with detailed proofs and illustrative examples, this book opens a view to the largely unexplored area of nonlinear systems with uncertainties--adaptive backstepping.

On the use of contraction theory for the design of nonlinear observers for ocean vehicles

  • J. JouffroyJ. Lottin
  • Mathematics
    Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)
  • 2002
This paper addresses the question of the applicability of contraction theory to the design of UGES observers for ocean vehicles by relation between the concept of exponential convergence of a contracting system and uniform global exponential stability (UGES).

On Stability in the Large for Systems of Ordinary Differential Equations

  • P. Hartman
  • Mathematics
    Canadian Journal of Mathematics
  • 1961
Autonomous systems. This note concerns the stability of systems of (real) differential equations in the large on Euclidean space En and on certain Riemannian manifolds Mn . The results will be

Nonlinear performance of a PI controlled missile: an explanation

Considers the practical interest of an approach to nonlinear system analysis. Based on the incremental norm, this approach proposes performance and robustness analysis criteria. Using computationally

Robust Nonlinear Control Design

The method sets forth the steps of chamber-drying the gas, monitoring the chamber-charged condition, shunting gas away from the receiver thereafter, and depressurizing and venting of the chamber.

Contraction analysis of nonlinear systems