Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference.
Yakar, Coşkun (2010)
Abstract and Applied Analysis
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Displaying similar documents to “Stability analysis of fractional differential systems with order lying in .”
Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference.
Exact solution of impulse response to a class of fractional oscillators and its stability.
Li, Ming, Lim, S.C., Chen, Shengyong (2011)
Mathematical Problems in Engineering
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Design of unknown input fractional-order observers for fractional-order systems
Ibrahima N'Doye, Mohamed Darouach, Holger Voos, Michel Zasadzinski (2013)
International Journal of Applied Mathematics and Computer Science
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This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach,...
Fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative
Tadeusz Kaczorek, Kamil Borawski (2016)
International Journal of Applied Mathematics and Computer Science
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The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.
Robust stabilization of fractional-order systems with interval uncertainties via fractional-order controllers.
Delshad, Saleh Sayyad, Asheghan, Mohammad Mostafa, Beheshti, Mohammadtaghi Hamidi (2010)
Advances in Difference Equations [electronic only]
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On Riemann-Liouville and Caputo derivatives.
Li, Changpin, Qian, Deliang, Chen, Yangquan (2011)
Discrete Dynamics in Nature and Society
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On fractional derivatives
Helena Musielak (1973)
Colloquium Mathematicae
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On a sum of fractional parts
B. Martić (1964)
Matematički Vesnik
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An analysis of the stability boundary for a linear fractional difference system
Tomáš Kisela (2015)
Mathematica Bohemica
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This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional...
Note on the fractional parts of λθⁿ
Masayoshi Hata (2005)
Acta Arithmetica
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Stability of Caputo fractional differential equations by Lyapunov functions
Ravi P. Agarwal, Donal O&#039;Regan, Snezhana Hristova (2015)
Applications of Mathematics
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The stability of the zero solution of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov-like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov-like function along the given fractional equation. Comparison results using this definition for scalar fractional differential equations are presented. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability, based...
Simple conditions for practical stability of positive fractional discrete-time linear systems
Mikołaj Busłowicz, Tadeusz Kaczorek (2009)
International Journal of Applied Mathematics and Computer Science
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In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated...