A stability test for non-commensurate fractional order systems

Systems and Control Letters

Volumn 62, Issue 9, 2013, Pages 739-746

  Sabatier, Jocelyn ^a   Farges, Christophe ^a   Trigeassou, Jean Claude ^a  

^a UNIVERSITÉ DE BORDEAUX   (France)

Author keywords

Cauchy's theorem; Non commensurate fractional order systems; Stability

Indexed keywords

A-STABILITY; BOUNDED INPUT; CAUCHY'S THEOREM; FRACTIONAL-ORDER SYSTEMS; ITS EFFICIENCIES; NUMERICAL EXAMPLE; OUTPUT STABILITY; SUFFICIENT CONDITIONS;

CONTROL; CONVERGENCE OF NUMERICAL METHODS; ELECTRICAL ENGINEERING;

ALGEBRA;

EID: 84879618530     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2013.04.008     Document Type: Article

References (17)

1. D. Matignon, Stability results on fractional differential equations with applications to control processing, in: Computational Engineering in Systems Applications, Vol. 2, Lille, France, 1996, pp. 963-968.
2. M. Moze, J. Sabatier, A. Oustaloup, LMI tools for stability analysis of fractional systems, in: 20th ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Technical Conference, ASME IDETC/CIE'05, Long Beach, California, USA, 2005.
3. J. Sabatier, M. Moze, and C. Farges LMI stability conditions for fractional order systems Computers & Mathematics with Applications 59 5 2010 1594 1609 10.1016/j.camwa.2009.08.003
4. C. Farges, M. Moze, and J. Sabatier Pseudo-state feedback stabilization of commensurate fractional order systems Automatica 46 10 2010 1730 1734 10.1016/j.automatica.2010.06.038
5. J.-C. Trigeassou, N. Maamri, J. Sabatier, and A. Oustaloup A Lyapunov approach to the stability of fractional differential equations Signal Processing 91 3 2011 437 445 10.1016/j.sigpro.2010.04.024
6. C. Farges, J. Sabatier, and M. Moze Fractional order polytopic systems: robust stability and stabilisation Advances in Difference Equations 35 2011 10.1186/1687-1847-2011-35
7. S. Skaar, A. Michel, and R. Miller Stability of viscoelastic control systems IEEE Transactions on Automatic Control 33 4 1988 348 357
8. C. Bonnet, and J. Partington Coprime factorizations and stability of fractional differential systems Systems & Control Letters 41 3 2000 167 174
9. C. Bonnet, and J. Partington Analysis of fractional delay systems of retarded and neutral type Automatica 38 7 2002 1133 1138 (Pubitemid 34524669)
10. C. Hwang, and Y. Cheng A numerical algorithm for stability testing of fractional delay systems Automatica 42 5 2006 825 831
11. J. Trigeassou, A. Benchellal, N. Maamri, and T. Poinot A frequency approach to the stability of fractional differential equations Transactions on Systems, Signals & Devices 4 1 2009 1 25
12. A. Oustaloup La Dérivation Non Entiére: Théorie, Synthése et Applications 1995 Hermés Paris
13. R. Malti, P. Melchior, P. Lanusse, A. Oustaloup, Towards an object oriented CRONE toolbox for fractional differential systems, in: 18th IFAC World Congress, Milan, Italy, 2011.
14. S.G. Krantz Handbook of Complex Variables 1999 (Chapter 5). The Argument Principle
15. H. Beyer, and S. Kempfle Definition of physically consistent damping laws with fractional derivatives Journal of Applied Mathematics and Mechanics 75 8 1995 623 635
16. B. Gross, and E. Braga Singularities of linear system functions Journal of Applied Mathematics and Mechanics 43 4-5 1963 244 245
17. H. Nyquist Regeneration theory Bell System Technical Journal 11 1932 126 147