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Robust Stability Analysis of Linear Parameter Varying Systems

Assanimoghaddam, Mehran (2012) Robust Stability Analysis of Linear Parameter Varying Systems. Master's, Fachhochschule Hannover.

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Abstract

The robust stability analysis of nonlinear systems is a complex and challenging task. A well-known method to analyse them is the Monte-Carlo simulation. However, analysing a system in such a statistical manner can be very time consuming and there is no guarantee that the worst-case is actually found. An alternative approach is to represent the nonlinear system in the framework of linear parameter varying (LPV) systems. The present work studies the stability of LPV systems with a focus on time-variant parameters with bounded variation rates. Based on the existence of parameter dependent Lyapunov functions, a concept of analysing LPV systems is presented. Unlike the Monte-Carlo simulation, this concept provides sufficient conditions for stability. As part of this concept, an approach based on the Full Block S-Procedure is introduced. With this procedure, it is possible to reduce the model complexity at the cost of a more conservative system description. The Full Block S-Procedure requires a linear fractional representation of the LPV model and leads to a feasibility problem with linear matrix inequalities. The resulting stability test allows to specify a trade-off between conservatism and computational effort. This trade-off is examined on two examples. The first is a controlled axis-1 model of a standard six axes industrial manipulator and the second is a model of a heaving and pitching airfoil.

Item URL in elib:https://elib.dlr.de/81897/
Document Type:Thesis (Master's)
Title:Robust Stability Analysis of Linear Parameter Varying Systems
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Assanimoghaddam, MehranMehran.Assanimoghaddam (at) dlr.deUNSPECIFIED
Date:September 2012
Refereed publication:No
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Number of Pages:59
Status:Published
Keywords:Linear Parameter Varying (LPV) Systems, Linear Fractional Representation (LFR), Linear Matrix Inequality (LMI), Full Block S-Procedure, Multipliers, Basis Functions, Conservatism
Institution:Fachhochschule Hannover
Department:Fakultät I - Elektro- und Informationstechnik
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Technik für Raumfahrtsysteme
DLR - Research theme (Project):R - Vorhaben Terrestrische Assistenz-Robotik
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of System Dynamics and Control > Space System Dynamics
Deposited By: Assanimoghaddam, Mehran
Deposited On:15 Apr 2013 09:48
Last Modified:12 Dec 2013 22:02

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