# 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…

## 21 Citations

### Towards backstepping design for incremental stability

- Mathematics49th IEEE Conference on Decision and Control (CDC)
- 2010

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

- EngineeringJournal of Dynamic Systems, Measurement, and Control
- 2019

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

- Mathematics2020 IEEE International Conference on Industrial Technology (ICIT)
- 2020

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

- MathematicsInt. J. Control
- 2017

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

- MathematicsIEEE Transactions on Automatic Control
- 2011

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

- Mathematics, Engineering2009 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

- Engineering, Mathematics
- 2013

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

- Engineering, MathematicsArXiv
- 2015

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.

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