Stability analysis of fractional differential system with Riemann–Liouville derivative

“…with the initial-value conditions When α 1 = α 2 = · · · = α n = α, the stability of system (4.17) has been studied in [2], the corresponding conclusion is as follows. Since system (4.17) is a linear one with a constant coefficient matrix, we can obtain the necessary and sufficient condition of the stability of the solution to this system.…”

Section: (B) Stability Analysismentioning

confidence: 99%

Equivalent system for a multiple-rational-order fractional differential system

Zhang

Kurths

et al. 2013

Phil. Trans. R. Soc. A.

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The equivalent system for a multiple-rational-order (MRO) fractional differential system is studied, where the fractional derivative is in the sense of Caputo or Riemann-Liouville. With the relationship between the Caputo derivative and the generalized fractional derivative, we can change the MRO fractional differential system with a Caputo derivative into a higher-dimensional system with the same Caputo derivative order lying in (0, 1). The stability of the zero solution to the original system is studied through the analysis of its equivalent system. For the RiemannLiouville case, we transform the MRO fractional differential system into a new one with the same order lying in (0, 1), where the properties of the RiemannLiouville derivative operator and the fractional integral operator are used. The corresponding stability is also studied. Finally, several numerical examples are provided to illustrate the derived results.

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“…For Caputo fractional derivative-based linear system, the stability results are formulated with fractional commensurate order of 0 < α < 1 and 1 < α < 2 in [2] and [3] respectively. In [4,5], the stability of fractional-order linear systems with Riemann-Liouville derivative is discussed with fractional commensurate order of 0 < α < 1 and 1 < α < 2. However, the results on the stability of fractional-order nonlinear systems are relatively few.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Fuzzy Control for Nonlinear Fractional-Order Uncertain Systems with Unknown Uncertainties and External Disturbance

Sun

2015

Entropy

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In this paper, the problem of robust control of nonlinear fractional-order systems in the presence of uncertainties and external disturbance is investigated. Fuzzy logic systems are used for estimating the unknown nonlinear functions. Based on the fractional Lyapunov direct method and some proposed Lemmas, an adaptive fuzzy controller is designed. The proposed method can guarantee all the signals in the closed-loop systems remain bounded and the tracking errors converge to an arbitrary small region of the origin. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.

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Stability analysis of fractional differential system with Riemann–Liouville derivative

Cited by 202 publications

References 3 publications

Analytical studies for linear periodic systems of fractional order

Analytical studies for linear periodic systems of fractional order

Equivalent system for a multiple-rational-order fractional differential system

Adaptive Fuzzy Control for Nonlinear Fractional-Order Uncertain Systems with Unknown Uncertainties and External Disturbance

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