Abstract
In the paper the Grunwald–Letnikov-type linear fractional variable order discrete-time systems are studied. The conditions for stability and instability are formulated. The regions of the systems stability are determined accordingly to locus of eigenvalues of a matrix associated to the considered system.DOI: http://dx.doi.org/10.5755/j01.eie.24.5.21846
Highlights
AND PRELIMINARIESRecently, theory of fractional dynamical systems has become one of the essential tool for modelling in various technical disciplines, in electrotechnics, chemistry, electrochemistry or viscoelasticity, see for instance [1]–[3]
We determined the regions of location of eigenvalues of matrices associated to the systems in order to guarantee the asymptotic stability of the considered systems
We investigate systems described by the Grünwald-Letnikov operator of convolution type, and with step h 0
Summary
AND PRELIMINARIESRecently, theory of fractional dynamical systems has become one of the essential tool for modelling in various technical disciplines, in electrotechnics, chemistry, electrochemistry or viscoelasticity, see for instance [1]–[3]. The systems with the fractional variable orders for continuous-time as well for discrete-time have been studied in [4]–[8]. We formulate and prove the conditions for the stability of the considered discrete-time systems.
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