Stability criteria for a class of fractional order systems

Nonlinear Dynamics

Volumn 61, Issue 1-2, 2010, Pages 153-161

  Kheirizad, Iraj ^a   Tavazoei, Mohammad Saleh ^b   Jalali, Ali Akbar ^a  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

^b SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Fractional order system; Stability; Stabilization

Indexed keywords

ALGEBRAIC CONDITIONS; BIBO STABILITY; CHARACTERISTIC EQUATION; FRACTIONAL ORDER; FRACTIONAL ORDER SYSTEM; FRACTIONAL-ORDER CHAOTIC SYSTEMS; FRACTIONAL-ORDER SYSTEMS; STABILITY PROBLEM; SYSTEM EQUATIONS;

ALGEBRA; CHAOTIC SYSTEMS; STABILITY CRITERIA; STABILIZATION;

SYSTEM STABILITY;

EID: 77954349733     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-009-9638-1     Document Type: Article

References (33)

1. H. Sun W. Chen Y.Q. Chen 2009 Variable-order fractional differential operators in anomalous diffusion modeling Phys. A: Stat. Mech. Appl. 388 4586 4592 10.1016/j.physa.2009.07.024
2. N. Bertrand J. Sabatier O. Briat J.M. Vinassa 2009 Fractional non-linear modelling of ultracapacitors Commun. Nonlinear Sci. Numer. Simul. 10.1016/j.cnsns.2009.05.066. In press
3. M.S. Tavazoei M. Haeri S. Jafari S. Bolouki M. Siami 2008 Some applications of fractional calculus in suppression of chaotic oscillations IEEE Trans. Ind. Electron. 55 11 4098 4101 10.1109/TIE.2008.925774
4. V. Feliu-Batlle R. Rivas Perez L. Sanchez Rodrigue 2007 Fractional robust control of main irrigation canals with variable dynamic parameters Control Eng. Pract. 15 673 686 10.1016/j.conengprac.2006.11.018 (Pubitemid 46357262)
5. Matignon, D.: Stability results for fractional differential equations with applications to control processing. In: Computational Engineering in Systems and Application Multi-conference, vol. 2, IMACS, IEEE-SMC Proceedings, pp. 963-968, Lille, France (July 1996)
6. D. Matignon 1998 Stability properties for generalized fractional differential systems ESAIM: Proc. 5 145 158 0920.34010 10.1051/proc:1998004 1665568
7. Sabatier, J., Moze, M., Farges, C.: On stability of fractional order systems. In: Third IFAC Workshop on Fractional Differentiation and its Applications (FDA'08), Ankara, Turkey (November 2008)
8. C. Li Z. Zhao 2009 Asymptotical stability analysis of linear fractional differential systems J. Shanghai Univ. (Engl. Ed). 13 3 197 206 10.1007/s11741-009-0302-1
9. W. Deng C. Li Q. Guo 2007 Analysis of fractional differential equations with multi-orders Fractals 15 173 182 1176.34008 10.1142/S0218348X07003472 2332373 (Pubitemid 46970248)
10. C. Bonnet J.R. Partington 2000 Coprime factorizations and stability of fractional differential systems Syst. Control Lett. 41 167 174 0985.93048 10.1016/S0167-6911(00)00050-5 1831424
11. Y.Q. Chen K.L. Moore 2002 Analytical stability bound for a class of delayed fractional order dynamic systems Nonlinear Dyn. 29 191 200 1020.34064 10.1023/A:1016591006562 1926474 (Pubitemid 34945398)
12. W. Deng C. Li J. Lü 2007 Stability analysis of linear fractional differential system with multiple time delays Nonlinear Dyn. 48 409 416 1185.34115 10.1007/s11071-006-9094-0 (Pubitemid 46407957)
13. C. Hwang Y. Cheng 2006 A numerical algorithm for stability testing of fractional delay systems Automatica 42 825 831 1137.93375 10.1016/j.automatica. 2006.01.008 2207823
14. H.S. Ahn Y.Q. Chen 2008 Necessary and sufficient stability condition of fractional order interval linear systems Automatica 44 2985 2988 1152.93455 10.1016/j.automatica.2008.07.003 2527230
15. M.S. Tavazoei M. Haeri 2009 A note on the stability of fractional order systems Math. Comput. Simul. 79 1566 1576 1168.34036 10.1016/j.matcom.2008.07. 003 2488105
16. Y.Q. Chen H.S. Ahn I. Podlubny 2006 Robust stability check of fractional order linear time invariant systems with interval uncertainties Signal Process. 86 2611 2618 1172.94385 10.1016/j.sigpro.2006.02.011 (Pubitemid 44026624)
17. M.S. Tavazoei M. Haeri S. Bolouki M. Siami 2008 Stability preservation analysis for frequency based methods in numerical simulation of fractional order systems SIAM J. Numer. Anal. 47 321 338 10.1137/080715949 2475942
18. M.S. Tavazoei M. Haeri 2009 Rational approximations in the simulation and implementation of fractional order dynamics: A descriptor system approach Automatica 10.1016/j.automatica.2009.09.016. In press
19. Y. Li Y.Q. Chen I. Podlubny 2009 Mittag-Leffler stability of fractional order nonlinear dynamic systems Automatica 45 1965 1969 1185.93062 10.1016/j.automatica.2009.04.003
20. X.J. Wen Z.M. Wu J.G. Lu 2008 Stability analysis of a class of nonlinear fractional order systems IEEE Trans. Circuits Syst. II 55 1178 1182 10.1109/TCSII.2008.2002571
21. M.S. Tavazoei 2009 Comments on "Stability analysis of a class of nonlinear fractional order systems" IEEE Trans. Circuits Syst. II 56 519 520 10.1109/TCSII.2009.2020944
22. Y. Li Y.Q. Chen I. Podlubny 2009 Stability of fractional order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag Leffler stability Comput. Math. Appl. 10.1016/j.camwa.2009.08.019. In press
23. I. Petras 2009 Stability of fractional order systems with rational orders: A survey Fract. Calc. Appl. Anal. 12 269 298 1182.26017 2572711
24. Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins University Press, Baltimore (1996)
25. T.Z. Huang 1998 Stability criteria for matrices Automatica 34 5 637 639 0937.93018 10.1016/S0005-1098(97)00234-3 1627994
26. S.E. Hamamci 2007 An algorithm for stabilization of fractional order time delay systems using fractional order PID controllers IEEE Trans. Automat. Contr. 52 1964 1969 10.1109/TAC.2007.906243 2358766 (Pubitemid 350130541)
27. S.E. Hamamci 2008 Stabilization using fractional order PI and PID controllers Nonlinear Dyn. 51 1-2 329 343 1170.93023
28. C. Bonnet J.R. Partington 2007 Stabilization of some fractional delay systems of neutral type Automatica 43 2047 2053 1138.93049 10.1016/j.automatica. 2007.03.017 2571731 (Pubitemid 350148069)
29. C. Li G. Peng 2004 Chaos in Chen's system with a fractional order Chaos Solitons Fractals 22 443 450 1060.37026 10.1016/j.chaos.2004.02.013 2060878
30. M.S. Tavazoei M. Haeri 2007 A necessary condition for double scroll attractor existence in fractional order systems Phys. Lett. A 367 1-2 102 113 10.1016/j.physleta.2007.05.081
31. M.S. Tavazoei M. Haeri S. Jafari 2008 Fractional controller to stabilize fixed points of uncertain chaotic systems: theoretical and experimental study Proc. Inst. Mech. Eng., Part I, J. Syst. Control Eng. 222 175 184 10.1243/09596518JSCE481
32. E. Ahmed A.M.A. El-Sayed H.A.A. El-Saka 2007 Equilibrium points, stability and numerical solutions of fractional order predator-prey and rabies models J. Math. Anal. Appl. 325 542 553 1105.65122 10.1016/j.jmaa.2006.01.087 2273544 (Pubitemid 44615337)
33. M.S. Tavazoei M. Haeri 2008 Chaotic attractors in incommensurate fractional order systems Phys. D: Nonlinear Phenom. 237 2628 2637 1157.26310 10.1016/j.physd.2008.03.037 2514122