Displaying similar documents to “Application of the Drazin inverse to the analysis of descriptor fractional discrete–time linear systems with regular pencils”

Descriptor fractional linear systems with regular pencils

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.

Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

Tadeusz Kaczorek (2013)

International Journal of Applied Mathematics and Computer Science

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The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.

Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems

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.

Minimum energy control of descriptor fractional discrete-time linear systems with two different fractional orders

Łukasz Sajewski (2017)

International Journal of Applied Mathematics and Computer Science

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Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass-Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is...

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,...

Duplication in a model of rock fracture with fractional derivative without singular kernel

Emile F. Doungmo Goufo, Morgan Kamga Pene, Jeanine N. Mwambakana (2015)

Open Mathematics

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We provide a mathematical analysis of a break-up model with the newly developed Caputo-Fabrizio fractional order derivative with no singular kernel, modeling rock fracture in the ecosystem. Recall that rock fractures play an important role in ecological and geological events, such as groundwater contamination, earthquakes and volcanic eruptions. Hence, in the theory of rock division, especially in eco-geology, open problems like phenomenon of shattering, which remains partially unexplained...

Minimum energy control of positive continuous-time linear systems with bounded inputs

Tadeusz Kaczorek (2013)

International Journal of Applied Mathematics and Computer Science

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The minimum energy control problem for positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.

Fractional positive continuous-time linear systems and their reachability

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.