Mittag–Leffler stability of fractional order nonlinear dynamic systems
In this paper, we propose the definition of Mittag–Leffler stability and introduce the fractional Lyapunov direct method. Fractional comparison principle is introduced and the application of Riemann–Liouville fractional order systems is extended by using Caputo fractional order systems. Two illustra...
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| Published in | Automatica (Oxford) Vol. 45; no. 8; pp. 1965 - 1969 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier Ltd
01.08.2009
Elsevier |
| Subjects | |
| Online Access | Get full text |
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| Abstract | In this paper, we propose the definition of Mittag–Leffler stability and introduce the fractional Lyapunov direct method. Fractional comparison principle is introduced and the application of Riemann–Liouville fractional order systems is extended by using Caputo fractional order systems. Two illustrative examples are provided to illustrate the proposed stability notion. |
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| AbstractList | In this paper, we propose the definition of Mittag-Leffler stability and introduce the fractional Lyapunov direct method. Fractional comparison principle is introduced and the application of Riemann-Liouville fractional order systems is extended by using Caputo fractional order systems. Two illustrative examples are provided to illustrate the proposed stability notion. |
| Author | Podlubny, Igor Chen, YangQuan Li, Yan |
| Author_xml | – sequence: 1 givenname: Yan surname: Li fullname: Li, Yan organization: Institute of Applied Math, School of Mathematics and System Sciences, Shandong University, Jinan 250100, PR China – sequence: 2 givenname: YangQuan surname: Chen fullname: Chen, YangQuan email: yqchen@ieee.org, yqchen@ece.usu.edu organization: Center for Self-Organizing and Intelligent Systems (CSOIS), Electrical and Computer Engineering Department, Utah State University, Logan, UT 84322-4160, USA – sequence: 3 givenname: Igor surname: Podlubny fullname: Podlubny, Igor organization: Department of Applied Informatics and Process Control, Faculty BERG, Technical University of Kosice, B. Nemcovej 3, 04200 Kosice, Slovak Republic |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21754711$$DView record in Pascal Francis |
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| CODEN | ATCAA9 |
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| Cites_doi | 10.1002/mma.190 10.1155/S0161171204312366 10.1109/TCT.1971.1083337 10.1023/A:1016591006562 10.1109/9.739144 10.1016/j.amc.2006.08.163 10.2514/3.8142 10.1142/S0129167X07004102 10.1007/s00397-005-0043-5 10.1080/10652460108819360 10.3182/20060719-3-PT-4902.00081 |
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| Issue | 8 |
| Keywords | Nonautonomous system Fractional Lyapunov direct method Fractional comparison principle Fractional order dynamic system Mittag–Leffler stability Stability Mittag-Leffler stability Non linear control Non autonomous system Dynamical system Fractional derivative Lyapunov function |
| Language | English |
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| References | Li, Y., Chen, Y. Q., Podlubny, I., & Cao, Y. (2008). Mittag-leffler stability of fractional order nonlinear dynamic systems. In Podlubny, Heymans (b15) 2006; 45 Miller, Samko (b10) 2001; 12 Podlubny (b12) 1999; 44 Tarasov (b18) 2007; 18 Chua (b5) 1971; CT-18 Cohen, Golding, Ron, Ben-Jacob (b6) 2001; 24 Sabatier, J. (2008). On stability of fractional order systems. In Chen, Y. Q. (2006). Ubiquitous fractional order controls? In Zhang, Li, Chen (b20) 2005; 21 Bagley, Torvik (b2) 1983; 27 Momani, Hadid (b11) 2004; 47 Sabatier, Agrawal, Tenreiro Machado (b17) 2007 Xu, Tan (b19) 2006; 49 Chen, Moore (b4) 2002; 29 Podlubny (b14) 2002; 5 Khalil (b7) 2002 Podlubny (b13) 1999 Bagley, Torvik (b1) 1983; 21 Li, Deng (b9) 2007; 187 10.1016/j.automatica.2009.04.003_b3 10.1016/j.automatica.2009.04.003_b16 Podlubny (10.1016/j.automatica.2009.04.003_b14) 2002; 5 10.1016/j.automatica.2009.04.003_b8 Miller (10.1016/j.automatica.2009.04.003_b10) 2001; 12 Chen (10.1016/j.automatica.2009.04.003_b4) 2002; 29 Cohen (10.1016/j.automatica.2009.04.003_b6) 2001; 24 Xu (10.1016/j.automatica.2009.04.003_b19) 2006; 49 Zhang (10.1016/j.automatica.2009.04.003_b20) 2005; 21 Podlubny (10.1016/j.automatica.2009.04.003_b12) 1999; 44 Podlubny (10.1016/j.automatica.2009.04.003_b13) 1999 Khalil (10.1016/j.automatica.2009.04.003_b7) 2002 Li (10.1016/j.automatica.2009.04.003_b9) 2007; 187 Tarasov (10.1016/j.automatica.2009.04.003_b18) 2007; 18 Bagley (10.1016/j.automatica.2009.04.003_b2) 1983; 27 Momani (10.1016/j.automatica.2009.04.003_b11) 2004; 47 Chua (10.1016/j.automatica.2009.04.003_b5) 1971; CT-18 Bagley (10.1016/j.automatica.2009.04.003_b1) 1983; 21 Podlubny (10.1016/j.automatica.2009.04.003_b15) 2006; 45 Sabatier (10.1016/j.automatica.2009.04.003_b17) 2007 |
| References_xml | – volume: 24 start-page: 1429 year: 2001 end-page: 1468 ident: b6 article-title: Bio-uiddynamics of lubricating bacteria publication-title: Mathematical Methods in the Applied Sciences – volume: 49 start-page: 257 year: 2006 end-page: 272 ident: b19 article-title: Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics publication-title: Science in China: Series G Physics, Mechanics and Astronomy – year: 2002 ident: b7 article-title: Nonlinear systems – volume: 18 start-page: 281 year: 2007 end-page: 299 ident: b18 article-title: Fractional derivative as fractional power of derivative publication-title: International Journal of Mathematics – year: 2007 ident: b17 article-title: Advances in fractional calculus — Theoretical developments and applications in physics and engineering – volume: 21 start-page: 741 year: 1983 end-page: 748 ident: b1 article-title: Fractional calculus — A different approach to the analysis of viscoelastically damped structures publication-title: AIAA Journal – volume: 27 start-page: 201 year: 1983 end-page: 210 ident: b2 article-title: A theoretical basis for the application of fractional calculus to viscoelasticity publication-title: Journal of Theology – volume: 47 start-page: 2503 year: 2004 end-page: 2507 ident: b11 article-title: Lyapunov stability solutions of fractional integrodifferential equations publication-title: International Journal of Mathematics and Mathematical Sciences – volume: 5 start-page: 367 year: 2002 end-page: 386 ident: b14 article-title: Geometric and physical interpretation of fractional integration and fractional differentiation publication-title: Fractional Calculus and Applied Analysis – volume: 12 start-page: 389 year: 2001 end-page: 402 ident: b10 article-title: Completely monotonic functions publication-title: Integral Transforms and and Special Functions – reference: Chen, Y. Q. (2006). Ubiquitous fractional order controls? In – volume: 44 start-page: 208 year: 1999 end-page: 214 ident: b12 article-title: Fractional-order systems and publication-title: IEEE Transactions on Automatic Control – reference: Li, Y., Chen, Y. Q., Podlubny, I., & Cao, Y. (2008). Mittag-leffler stability of fractional order nonlinear dynamic systems. In – year: 1999 ident: b13 article-title: Fractional differential equations – reference: Sabatier, J. (2008). On stability of fractional order systems. In – volume: 187 start-page: 777 year: 2007 end-page: 784 ident: b9 article-title: Remarks on fractional derivatives publication-title: Applied Mathematics and Computation – volume: 45 start-page: 765 year: 2006 end-page: 772 ident: b15 article-title: Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives publication-title: Rheologica Acta – volume: 29 start-page: 191 year: 2002 end-page: 200 ident: b4 article-title: Analytical stability bound for a class of delayed fractional order dynamic systems publication-title: Nonlinear Dynamics – volume: CT-18 start-page: 507 year: 1971 end-page: 519 ident: b5 article-title: Memristor — The missing circuit element publication-title: IEEE Transactions on Circuit Theory – volume: 21 year: 2005 ident: b20 article-title: Extension of Lyapunov second method by fractional calculus publication-title: Pure and Applied Mathematics – volume: 24 start-page: 1429 year: 2001 ident: 10.1016/j.automatica.2009.04.003_b6 article-title: Bio-uiddynamics of lubricating bacteria publication-title: Mathematical Methods in the Applied Sciences doi: 10.1002/mma.190 – volume: 49 start-page: 257 issue: 3 year: 2006 ident: 10.1016/j.automatica.2009.04.003_b19 article-title: Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics publication-title: Science in China: Series G Physics, Mechanics and Astronomy – volume: 47 start-page: 2503 year: 2004 ident: 10.1016/j.automatica.2009.04.003_b11 article-title: Lyapunov stability solutions of fractional integrodifferential equations publication-title: International Journal of Mathematics and Mathematical Sciences doi: 10.1155/S0161171204312366 – volume: 21 issue: 3 year: 2005 ident: 10.1016/j.automatica.2009.04.003_b20 article-title: Extension of Lyapunov second method by fractional calculus publication-title: Pure and Applied Mathematics – year: 2002 ident: 10.1016/j.automatica.2009.04.003_b7 – volume: 5 start-page: 367 issue: 4 year: 2002 ident: 10.1016/j.automatica.2009.04.003_b14 article-title: Geometric and physical interpretation of fractional integration and fractional differentiation publication-title: Fractional Calculus and Applied Analysis – volume: CT-18 start-page: 507 issue: 5 year: 1971 ident: 10.1016/j.automatica.2009.04.003_b5 article-title: Memristor — The missing circuit element publication-title: IEEE Transactions on Circuit Theory doi: 10.1109/TCT.1971.1083337 – volume: 29 start-page: 191 year: 2002 ident: 10.1016/j.automatica.2009.04.003_b4 article-title: Analytical stability bound for a class of delayed fractional order dynamic systems publication-title: Nonlinear Dynamics doi: 10.1023/A:1016591006562 – ident: 10.1016/j.automatica.2009.04.003_b8 – volume: 44 start-page: 208 issue: 1 year: 1999 ident: 10.1016/j.automatica.2009.04.003_b12 article-title: Fractional-order systems and PIλDμ-controllers publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.739144 – volume: 187 start-page: 777 issue: 2 year: 2007 ident: 10.1016/j.automatica.2009.04.003_b9 article-title: Remarks on fractional derivatives publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2006.08.163 – ident: 10.1016/j.automatica.2009.04.003_b16 – volume: 21 start-page: 741 issue: 5 year: 1983 ident: 10.1016/j.automatica.2009.04.003_b1 article-title: Fractional calculus — A different approach to the analysis of viscoelastically damped structures publication-title: AIAA Journal doi: 10.2514/3.8142 – volume: 18 start-page: 281 issue: 3 year: 2007 ident: 10.1016/j.automatica.2009.04.003_b18 article-title: Fractional derivative as fractional power of derivative publication-title: International Journal of Mathematics doi: 10.1142/S0129167X07004102 – year: 2007 ident: 10.1016/j.automatica.2009.04.003_b17 – volume: 27 start-page: 201 issue: 3 year: 1983 ident: 10.1016/j.automatica.2009.04.003_b2 article-title: A theoretical basis for the application of fractional calculus to viscoelasticity publication-title: Journal of Theology – volume: 45 start-page: 765 issue: 5 year: 2006 ident: 10.1016/j.automatica.2009.04.003_b15 article-title: Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives publication-title: Rheologica Acta doi: 10.1007/s00397-005-0043-5 – year: 1999 ident: 10.1016/j.automatica.2009.04.003_b13 – volume: 12 start-page: 389 issue: 4 year: 2001 ident: 10.1016/j.automatica.2009.04.003_b10 article-title: Completely monotonic functions publication-title: Integral Transforms and and Special Functions doi: 10.1080/10652460108819360 – ident: 10.1016/j.automatica.2009.04.003_b3 doi: 10.3182/20060719-3-PT-4902.00081 |
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| Snippet | In this paper, we propose the definition of Mittag–Leffler stability and introduce the fractional Lyapunov direct method. Fractional comparison principle is... In this paper, we propose the definition of Mittag-Leffler stability and introduce the fractional Lyapunov direct method. Fractional comparison principle is... |
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| SubjectTerms | Applied sciences Automation Computer science; control theory; systems Control system analysis Control theory. Systems Dynamical systems Exact sciences and technology Fractional comparison principle Fractional Lyapunov direct method Fractional order dynamic system Mittag–Leffler stability Nonautonomous system Nonlinear dynamics Stability |
| Title | Mittag–Leffler stability of fractional order nonlinear dynamic systems |
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