Reference : A New Polytopic Approach for the Unknown Input Functional Observer Design

	Document type :	Scientific journals : Article
	Discipline(s) :	Engineering, computing & technology : Electrical & electronics engineering
	Focus Areas :	Security, Reliability and Trust
	To cite this reference:	http://hdl.handle.net/10993/32860

Title :	A New Polytopic Approach for the Unknown Input Functional Observer Design
Language :	English
Author, co-author :	Bezzaoucha, Souad [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]
	Voos, Holger [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
	Darouach, Mohamed []
Publication date :	Jan-2017
Journal title :	International Journal of Control
Publisher :	Taylor & Francis Ltd
Peer reviewed :	Yes (verified by ORBilu)
Audience :	International
ISSN :	0020-7179
Keywords :	[en] Functional Observers Design ; Nonlinear Systems ; Takagi-Sugeno Polytopic Representation ; Linear Matrix Inequality ; Waste Water Treatment Plant ; UAV control
Abstract :	[en] In this paper, a constructive procedure to design Functional Unknown Input Observers for nonlin ear continuous time systems is proposed under the Polytopic Takagi-Sugeno framework. An equivalent representation for the nonlinear model is achieved using the Sector Nonlinearity Transformation (SNT). Applying the Lyapunov theory and the L2 attenuation, Linear Matrix Inequalities (LMI)s conditions are deduced which are solved for feasibility to obtain the observer design matrices. To cope with the e ffect of unknown inputs, classical approach of decoupling the unknown input for the linear case is used. Both algebraic and solver based solutions are proposed (relaxed conditions). Necessary and su fficient conditions for the existence of the functional polytopic observer are given. For both approaches, the general and particular cases (measurable premise variables, full state estimation with full and reduced order cases) are considered and it is shown that the proposed conditions correspond to the one presented for standard linear case. To illustrate the proposed theoretical results, detailed numerical simulations are presented for a Quadrotor Aerial Robots Landing and a Waste Water Treatment Plant (WWTP). Both systems are highly nonlinear and represented in a T-S polytopic form with unmeasurable premise variables and unknown inputs.
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/32860
DOI :	10.1080/00207179.2017.1288299

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