2009
DOI: 10.1007/s11741-009-0302-1
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Abstract: It has been recently found that many models were established with the aid of fractional derivatives, such as viscoelastic systems, colored noise, electrode-electrolyte polarization, dielectric polarization, boundary layer effects in ducts, electromagnetic waves, quantitative finance, quantum evolution of complex systems, and fractional kinetics. In this paper, the asymptotical stability of higher-dimensional linear fractional differential systems with the Riemann-Liouville fractional order and Caputo fractiona… Show more

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Cited by 17 publications
(7 citation statements)
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“…Thus, It is interesting that the specific value (−2 α ) for Im w = 0 (or 1 − 2 α for Im v = 0) can be obtained analytically. We will show that, for α ∈ (0, 1), the interior of the unit circle is mapped by the transformations (20) or (21) into the interior of the FD stability contour, but this does not necessarily hold true for α ∈ (1, 2).…”
Section: Coordinate Transformationsmentioning
confidence: 93%
See 1 more Smart Citation
“…Thus, It is interesting that the specific value (−2 α ) for Im w = 0 (or 1 − 2 α for Im v = 0) can be obtained analytically. We will show that, for α ∈ (0, 1), the interior of the unit circle is mapped by the transformations (20) or (21) into the interior of the FD stability contour, but this does not necessarily hold true for α ∈ (1, 2).…”
Section: Coordinate Transformationsmentioning
confidence: 93%
“…Unlike for continuous-time LTI systems [20][21][22][23][24][25], stability analysis for fractional order discrete-time LTI state space systems has not been given due research attention. First stability results for FFD-based systems have included either (analytical) sufficient conditions only [10,15] or numerically in-efficient necessary and sufficient ones [10,15,26,27].…”
Section: Introductionmentioning
confidence: 99%
“…Thus, the stability analysis of FDEs becomes more important in future applications. However, most stability criteria on FDEs focus on linear FDEs with Caputo derivative or RiemannLiouville derivative [51][52][53]. In recent years, there has been some published work dealing with the stability of nonlinear FDEs.…”
Section: Remark 12mentioning
confidence: 99%
“…The FD and FFD [20] are often used in the context of modeling of discrete-time fractional-order LTI state space systems [14,[20][21][22]. It is the asymptotic stability that is considered the most important aspect of an analysis of fractional-order LTI systems [23][24][25][26][27][28]. As for continuous-time systems, the celebrated Matignon's stability criterion [29] has established a simple argument condition for eigenvalues of a state matrix.…”
Section: Introductionmentioning
confidence: 99%