01186nas a2200145   4500000000100000000000100001008004100002100002100043700001700064700002400081245009200105856007200197490000700269520076400276       2022                            d1 aTadeusz Kaczorek1 aJerzy Klamka1 aAndrzej Dzieliński00aControllability of linear convex combination of linear discrete-time fractional systems  uhttp://journals.pan.pl/Content/124861/PDF/2928_BPASTS_2022_70_5.pdf0 v703 a<p>In this paper the controllability properties of the convex linear combination of fractional, linear, discrete-time systems are characterized and investigated. The notions of linear convex combination and controllability in the context of fractional-order systems are recalled. Then, the controllability property of such a linear combination of discrete-time, linear fractional systems is proven. Further, the reduction of an infinite problem of transition matrix derivation is reduced to a finite one, which greatly simplifies the numerical burden of the controllability issue. Examples of controllable and uncontrollable, single-input, linear systems are presented. The possibility of extension of the considerations to multi-input systems is shown.</p>