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Stability analysis of fractional differential system with Riemann-Liouville derivative. (English) Zbl 1202.34020
Summary: We focus on establishing stability theorems for fractional differential system with Riemann-Liouville derivative, in particular our analysis covers the linear system, the perturbed system and the time-delayed system.

34A08Fractional differential equations
34D20Stability of ODE
45J05Integro-ordinary differential equations
Full Text: DOI
[1] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and application of fractional differential equations, (2006) · Zbl 1092.45003
[2] Oldham, K. B.; Spanier, J.: The fractional calculus, (1974) · Zbl 0292.26011
[3] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[4] Machado, J. A. T.: Analysis and design of fractional-order digital control systems, J. syst. Anal. modelling simul. 27, 107-122 (1997) · Zbl 0875.93154
[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 14, 247-257 (2008)
[6] Vinagre, B. M.; Monje, A. C.: Introducción al control fraccionario, Riai 3, 5-23 (2006)
[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. 39, 346-348 (2005)
[9] Deng, W. H.; Li, C. P.; Guo, Q.: Analysis of fractional differential equations with multi-orders, Fractals 15, 1-10 (2007) · Zbl 1176.34008
[10] Deng, W. H.; Li, C. P.; Lü, J. H.: Stability analysis of linear fractional differential system with multiple time delays, Nonlinear dynam. 48, 409-416 (2007) · Zbl 1185.34115 · doi:10.1007/s11071-006-9094-0
[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 6, 419-434 (2007) · Zbl 1125.93051 · doi:10.1007/978-1-4020-6042-7_29
[12] , Higher transcendental functions (1955)