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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| Vydáno v: | IET control theory & applications Ročník 12; číslo 3; s. 359 - 367 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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The Institution of Engineering and Technology
13.02.2018
Institution of Engineering and Technology |
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| ISSN: | 1751-8644, 1751-8652 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Boukal, Yassine Darouach, Mohamed Zasadzinski, Michel Radhy, Nour-Eddine |
| Author_xml | – sequence: 1 givenname: Yassine surname: Boukal fullname: Boukal, Yassine organization: 3Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines (LAMIH, UMR 8201, CNRS), Université de Valenciennes UVHC, Valenciennes, France – sequence: 2 givenname: Mohamed surname: Darouach fullname: Darouach, Mohamed organization: 1Centre de Recherche en Automatique de Nancy (CRAN - UMR 7039, CNRS), Université de Lorraine, IUT de Longwy, 186 rue de Lorraine 54400 Cosnes et Romain, France – sequence: 3 givenname: Michel surname: Zasadzinski fullname: Zasadzinski, Michel email: Michel.zasadzinski@univ-lorraine.fr organization: 1Centre de Recherche en Automatique de Nancy (CRAN - UMR 7039, CNRS), Université de Lorraine, IUT de Longwy, 186 rue de Lorraine 54400 Cosnes et Romain, France – sequence: 4 givenname: Nour-Eddine surname: Radhy fullname: Radhy, Nour-Eddine organization: 2Faculté des Sciences Ain-Chock, Laboratoire Physique et Matériaux Microélectronique Automatique et Thermique (LPMMAT), Université Hassan II, BP: 5366 Maarif, Casablanca 20100, Morocco |
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| Keywords | 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 |
| Language | English |
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| SubjectTerms | 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 |
| Title | Large-scale fractional-order systems: stability analysis and their decentralised functional observers design |
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