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A polytopic approach for the nonlinear unknown input functional observers design: Application to a quadrotor aerial robots landing

Souad Bezzaoucha, +2 more
- pp 1146-1152
TLDR
The proposed approach consists in rewriting the nonlinear model in a polytopic form applying the Sector Non-linearity Transformation (SNT) and then applying the proposed algorithm for the observer design.
Abstract: 
This paper considers a method of designing functional observers for continuous time nonlinear systems subject to unknown inputs. The proposed approach consists in rewriting the nonlinear model in a polytopic form (also known as multiple or Takagi-Sugeno models) applying the Sector Non-linearity Transformation (SNT) and then apply the proposed algorithm for the observer design. Sufficient conditions for the asymptotic stability of the estimation error are given in terms of linear matrix inequalities (LMls) and rank conditions. An application to a quadrotor aerial robots landing is then presented.

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A Polytopic Approach for the Nonlinear Unknown Input Functional
Observers Design: Application to a Quadrotor Aerial Robots Landing
Souad Bezzaoucha
1
, Holger Voos
1
and Mohamed Darouach
2
Abstract— This paper considers a method of designing func-
tional observers for continuous time nonlinear systems subject
to unknown inputs. The proposed approach consists in re-
writing the nonlinear model in a polytopic form (also known
as multiple or Takagi-Sugeno models) applying the Sector Non-
linearity Transformation (SNT) and then apply the proposed
algorithm for the observer design. Sufficient conditions for the
asymptotic stability of the estimation error are given in terms
of linear matrix inequalities (LMIs) and rank conditions.
An application to a quadrotor aerial robots landing is then
presented.
1
Souad Bezzaoucha and Holger Voos are with the Interdisciplinary
Centre for Security, Reliability and Trust (SnT), Automatic Control
Research Group, University of Luxembourg, Campus Kirchberg, 6
rue Coudenhove-Kalergi L-1359, Luxembourg souad.bezzaoucha,
holger.voos@uni.lu
2
Mohamed Darouach is with the Research Center for Auto-
matic Control of Nancy (CRAN), Universit
´
e de Lorraine, IUT de
Longwy, 186 rue de Lorraine, 54400 Cosnes et Romain, France
mohamed.darouach@univ-lorraine.fr
References
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Nonlinear observer design using Lyapunov's auxiliary theorem

Nikolaos Kazantzis, +1 more
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An approach to stability analysis of second order fuzzy systems

S. Kawamoto, +3 more
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Ali J. Koshkouei, +1 more
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TL;DR: In this paper, a sliding mode observer is designed to yield feedforward compensation input to stabilize the error estimation system with and without a Lipschitz nonlinearity, and sufficient conditions for stability of the Thau observer are also proposed.
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Reduced-order estimation Part 1. Filtering

K.M. Nagpal, +2 more
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TL;DR: In this article, a reduced-order Kalman filter is proposed for estimating the state of a Luenberger observer with respect to the noises in the system, where the filler is much like a Luinberger observer for the state to be estimated.
Journal ArticleDOI

Optimal unbiased filtering via linear matrix inequalities

James T. Watson, +1 more
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TL;DR: In this article, an explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix, where the order of the optimal filter is equal to the number of measurements.
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