author={J{\'e}r{\^o}me Jouffryo and Jacques Lottin},
  journal={IFAC Proceedings Volumes},
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… 

Towards backstepping design for incremental stability

This paper takes a step in this direction by developing a backstepping design approach to incremental stability by synthesizing a controller rendering a magnetic levitator incrementally stable.

Contraction Theory Approach to Disturbance Observer Based Filtered Backstepping Design

A new contraction theory-based technique to design a high gain disturbance observer-based filtered backstepping controller and to quantify the convergence bounds in terms of design parameters to achieve a satisfactory closed loop performance is proposed.

Controller and Observer Design using Vector Framework with Simplified Contraction Analysis

It is shown that by employing this simplified contraction analysis using vector framework, it is possible to design controller and observer in a simplified way.

Contraction-based stabilisation of nonlinear singularly perturbed systems and application to high gain feedback

A contraction theory-based framework is proposed for stabilisation of singularly perturbed systems and this framework provides relaxation over traditional quadratic Lyapunov-based method as there is no need to satisfy interconnection conditions during controller design algorithm.

Backstepping Design for Incremental Stability

A backstepping design approach for incremental stability is developed and it is shown that most of the existing controller design techniques provide controllers enforcing stability rather than incremental stability.

Contraction based adaptive control of a class of nonlinear systems

  • B. SharmaI. Kar
  • Mathematics, Engineering
    2009 American Control Conference
  • 2009
Adaptive control problem of nonlinear systems having dynamics in parametric strict feedback form is addressed here. Effort is made to derive adaptive methodology for controller design in contraction

UAV Flight Path Control Using Contraction-Based Back-stepping Control

In this paper, a contraction-based backstepping nonlinear control technique was proposed. The proposed controller synthesis technique utilizes both the recursive nature of backstepping control and of

A Contraction Theory Approach for Analysis of Performance Recovery in Dynamic Surface Control

This paper attempts to design a novel disturbance observer based dynamic surface controller using contraction framework and shows that DSC technique recover the performance of a backstepping controller for a small range of filter parameter but also derive the maximum bound for it.



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