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Positivity of fractional descriptor linear discrete-time systems

Kaczorek Tadeusz

International Journal of Applied Mathematics and Computer Science

2019

Vol. 29, no. 2

305--310

The positivity of fractional descriptor linear discrete-time systems is investigated. The solution to the state equation of the systems is derived. Necessary and sufficient conditions for the positivity of fractional descriptor linear discrete-time systems are established. The discussion is illustrated with numerical examples.

Reduced-order perfect nonlinear observers of fractional descriptor discrete-time nonlinear systems

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2017

Vol. 27, no. 2

245--251

The purpose of this work is to propose and characterize fractional descriptor reduced-order perfect nonlinear observers for a class of fractional descriptor discrete-time nonlinear systems. Sufficient conditions for the existence of these observers are established. The design procedure of the observers is given and demonstrated on a numerical example.

Fractional descriptor standard and positive discrete-time nonlinear systems

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2015

Vol. 63, nr 3

651--655

A method of analysis of the fractional descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on a numerical example.