Stability analysis of fractional differential system with Riemann-Liouville derivative

Mathematical and Computer Modelling

Volumn 52, Issue 5-6, 2010, Pages 862-874

  Qian, Deliang ^a   Li, Changpin ^a   Agarwal, Ravi P ^b,c   Wong, Patricia J Y ^d  

^a SHANGHAI UNIVERSITY   (China)

^b Florida Institute of Technology ^*  (United States)

^c KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

^d NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Fractional differential system; Mittag Leffler function; Riemann Liouville derivative; Stability

Indexed keywords

DERIVATIVE STABILITY; FRACTIONAL DIFFERENTIAL; MITTAG-LEFFLER FUNCTIONS; PERTURBED SYSTEMS; STABILITY ANALYSIS; STABILITY THEOREMS; TIME-DELAYED SYSTEMS;

DIFFERENTIAL EQUATIONS; FUNCTIONS; LINEAR SYSTEMS;

SYSTEM STABILITY;

EID: 77954177563     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2010.05.016     Document Type: Article

References (12)

1. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and Application of Fractional Differential Equations 2006, Elsevier, New York.
2. Oldham K.B., Spanier J. The Fractional Calculus 1974, Acadmic Press, New York, renewed, 2006.
3. Podlubny I. Fractional Differential Equations 1999, Academic Press, New York.
4. Machado J.A.T. Analysis and design of fractional-order digital control systems. J. Syst. Anal. Modelling Simul. 1997, 27:107-122.
5. Tavazoei M.S., Haeri M. Stabilization of unstable fixed points of chaotic fractional order systems by a state fractional PI controller. Eur. J. Control 2008, 14:247-257.
6. Vinagre B.M., Monje A.C. Introducción al control fraccionario. RIAI 2006, 3:5-23.
7. D. Matignon, Stability results for fractional differential equations with applications to control processing, Computational Engineering in Systems and Application Multiconference, IMACS, IEEE-SMC, Lille, France, vol. 2, 1996, pp. 963-968.
8. Zeng Q.S., Cao G.Y., Zhu X.J. The asympototic stability on sequential fractional-Order systems. J. Shanghai JiaoTong Univ. 2005, 39:346-348.
9. Deng W.H., Li C.P., Guo Q. Analysis of fractional differential equations with multi-orders. Fractals 2007, 15:1-10.
10. Deng W.H., Li C.P., Lü J.H. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynam. 2007, 48:409-416.
11. Moze M., Sabatier J., Oustaloup A. LMI Characterization of Fractional Systems Stability. Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering 2007, 6:419-434. Springer.
12. Higher Transcendental Functions 1955, McGraw Hill, New York. A. Erdélyi (Ed.).