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Bialystok, Poland

Kaczorek T.,Bialystok Technical University
International Journal of Applied Mathematics and Computer Science | Year: 2011

A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils. Source


Kaczorek T.,Bialystok Technical University
International Journal of Applied Mathematics and Computer Science | Year: 2012

The problem of the existence and determination of the set of Metzler matrices for given stable polynomials is formulated and solved. Necessary and sufficient conditions are established for the existence of the set of Metzler matrices for given stable polynomials. A procedure for finding the set of Metzler matrices for given stable polynomials is proposed and illustrated with numerical examples. Source


Kaczorek T.,Bialystok Technical University
International Journal of Applied Mathematics and Computer Science | Year: 2011

Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations. Source


The controllability and observability of linear electrical circuits composed of resistors, coils, capacitors and voltage (current) sources are addressed. It is shown that: 1) the linear electrical circuits are uncontrollable and unobservable if and only if their parameters satisfy some special conditions, 2) the uncontrollable pair (A,B) (unobservable pair (A,C)) of the electrical circuit can be decomposed into controllable (observable) and uncontrollable (unobservable) parts, 3) the transfer matrices of the uncontrollable electrical circuit are zero. The considerations are llustrated by examples of linear circuits. Source


Kaczorek T.,Bialystok Technical University
International Journal of Applied Mathematics and Computer Science | Year: 2013

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. Source

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