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Practical and asymptotic stabilities for a class of delayed fractional discrete-time linear systems

Ruszewski A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 3

509--515

The practical and asymptotic stabilities of delayed fractional discrete-time linear systems described by the model without a time shift in the difference are addressed. The D-decomposition approach is used for stability analysis. New necessary and sufficient stability conditions are established. The conditions in terms of the location of eigenvalues of the system matrix in the complex plane are given.

Singular Fractional Continuous-Time and Discrete-Time Linear Systems

Kaczorek T.

Acta Mechanica et Automatica

2013

Vol. 7, no. 1

26-33

New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example of singular fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and 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 systems if it contains at least one mesh consisting of branches with only ideal supercondensators and voltage sources or at least one node with branches with supercoils. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional discrete-time linear systems is derived. The considerations are illustrated by numerical examples.