Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models

The main aim of this paper is to present and compare three approaches to uncertainty modeling and robust stability analysis for fractional-order (FO) linear time-invariant (LTI) single-input single-output (SISO) uncertain systems. The investigated objects are described either via FO models with para...

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Main Authors: Radek Matušů, Bilal Şenol, Libor Pekař
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2018/8073481
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author Radek Matušů
Bilal Şenol
Libor Pekař
author_facet Radek Matušů
Bilal Şenol
Libor Pekař
author_sort Radek Matušů
collection DOAJ
description The main aim of this paper is to present and compare three approaches to uncertainty modeling and robust stability analysis for fractional-order (FO) linear time-invariant (LTI) single-input single-output (SISO) uncertain systems. The investigated objects are described either via FO models with parametric uncertainty, by means of FO unstructured multiplicative uncertainty models, or through FO unstructured additive uncertainty models, while the unstructured models are constructed on the basis of appropriate selection of a nominal plant and a weight function. Robust stability investigation for systems with parametric uncertainty uses the combination of plotting the value sets and application of the zero exclusion condition. For the case of systems with unstructured uncertainty, the graphical interpretation of the utilized robust stability test is based mainly on the envelopes of the Nyquist diagrams. The theoretical foundations are followed by two extensive, illustrative examples where the plant models are created; the robust stability of feedback control loops is analyzed, and obtained results are discussed.
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institution OA Journals
issn 1076-2787
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spelling doaj-art-e4d8dc18ff0743f280ac7dd15235dfad2025-08-20T02:21:18ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/80734818073481Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty ModelsRadek Matušů0Bilal Şenol1Libor Pekař2Centre for Security, Information and Advanced Technologies (CEBIA-Tech), Faculty of Applied Informatics, Tomas Bata University in Zlín, Nám. T. G. Masaryka 5555, 760 01 Zlín, Czech RepublicDepartment of Computer Engineering, Faculty of Engineering, Inonu University, 44280 Malatya, TurkeyCentre for Security, Information and Advanced Technologies (CEBIA-Tech), Faculty of Applied Informatics, Tomas Bata University in Zlín, Nám. T. G. Masaryka 5555, 760 01 Zlín, Czech RepublicThe main aim of this paper is to present and compare three approaches to uncertainty modeling and robust stability analysis for fractional-order (FO) linear time-invariant (LTI) single-input single-output (SISO) uncertain systems. The investigated objects are described either via FO models with parametric uncertainty, by means of FO unstructured multiplicative uncertainty models, or through FO unstructured additive uncertainty models, while the unstructured models are constructed on the basis of appropriate selection of a nominal plant and a weight function. Robust stability investigation for systems with parametric uncertainty uses the combination of plotting the value sets and application of the zero exclusion condition. For the case of systems with unstructured uncertainty, the graphical interpretation of the utilized robust stability test is based mainly on the envelopes of the Nyquist diagrams. The theoretical foundations are followed by two extensive, illustrative examples where the plant models are created; the robust stability of feedback control loops is analyzed, and obtained results are discussed.http://dx.doi.org/10.1155/2018/8073481
spellingShingle Radek Matušů
Bilal Şenol
Libor Pekař
Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models
Complexity
title Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models
title_full Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models
title_fullStr Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models
title_full_unstemmed Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models
title_short Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models
title_sort robust stability of fractional order linear time invariant systems parametric versus unstructured uncertainty models
url http://dx.doi.org/10.1155/2018/8073481
work_keys_str_mv AT radekmatusu robuststabilityoffractionalorderlineartimeinvariantsystemsparametricversusunstructureduncertaintymodels
AT bilalsenol robuststabilityoffractionalorderlineartimeinvariantsystemsparametricversusunstructureduncertaintymodels
AT liborpekar robuststabilityoffractionalorderlineartimeinvariantsystemsparametricversusunstructureduncertaintymodels