Stability analysis of fractional differential systems with order lying in .
Zhang, Fengrong, Li, Changpin (2011)
Advances in Difference Equations [electronic only]
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Zhang, Fengrong, Li, Changpin (2011)
Advances in Difference Equations [electronic only]
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Khazanov, V.B. (2005)
Zapiski Nauchnykh Seminarov POMI
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Delshad, Saleh Sayyad, Asheghan, Mohammad Mostafa, Beheshti, Mohammadtaghi Hamidi (2010)
Advances in Difference Equations [electronic only]
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Tadeusz Kaczorek (2013)
International Journal of Applied Mathematics and Computer Science
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Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.
Aleroev, T.S. (2005)
Sibirskij Matematicheskij Zhurnal
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Handelman, David (2007)
Fixed Point Theory and Applications [electronic only]
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Tadeusz Kaczorek (2013)
International Journal of Applied Mathematics and Computer Science
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Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.
Ilić, M., Turner, I.W., Anh, V. (2008)
Journal of Applied Mathematics and Stochastic Analysis
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Tadeusz Kaczorek (2010)
Control and Cybernetics
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Tadeusz Kaczorek (2008)
International Journal of Applied Mathematics and Computer Science
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A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive 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,...
Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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Masayoshi Hata (2005)
Acta Arithmetica
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