Large-scale fractional-order systems: stability analysis and their decentralised functional observers design

This study concerns the stability analysis of linear large-scale fractional-order systems and its functional observers design. First, based on the diffusive representation of the fractional-order derivative and the indirect Lyapunov approach, the stability of large-scale fractional-order interconnec...

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Bibliographic Details
Published in:IET control theory & applications Vol. 12; no. 3; pp. 359 - 367
Main Authors: Boukal, Yassine, Darouach, Mohamed, Zasadzinski, Michel, Radhy, Nour-Eddine
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 13.02.2018
Institution of Engineering and Technology
Subjects:
asymptotic stability
Automatic
control system synthesis
decentralised functional observers design
diffusive representation
Engineering Sciences
estimation error asymptotic stability
existence conditions
fractional‐order derivative
indirect Lyapunov approach
interconnected systems
large‐scale fractional‐order interconnected system stability
linear large‐scale fractional‐order systems
linear matrix inequalities
linear matrix inequality formulation
linear systems
LMI
multivariable systems
observers
observers gains matrices
Research Article
stability analysis
stability condition
linear large-scale fractional-order systems
estimation error asymptotic stability
observers gains matrices
stability analysis
large-scale fractional-order interconnected system stability
indirect Lyapunov approach
control system synthesis
LMI
linear systems
asymptotic stability
fractional-order derivative
stability condition
linear matrix inequality formulation
diffusive representation
linear matrix inequalities
multivariable systems
existence conditions
decentralised functional observers design
interconnected systems
observers
ISSN:1751-8644, 1751-8652
Online Access:Get full text
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Description
Summary:This study concerns the stability analysis of linear large-scale fractional-order systems and its functional observers design. First, based on the diffusive representation of the fractional-order derivative and the indirect Lyapunov approach, the stability of large-scale fractional-order interconnected systems is studied. Then, a sufficient stability condition of such systems is given in linear matrix inequality (LMI) formulation. In the second part of this work, the existence conditions of functional decentralised observers for this class of systems are given, and the asymptotic stability of estimation errors is investigated. The observers gains matrices are derived by solving the obtained LMI. Numerical examples are given to illustrate the validity of the proposed approach.
ISSN:1751-8644
1751-8652
DOI:10.1049/iet-cta.2017.0264