فهرست نشریات علمی دسترسی آزاد ایران

This paper examines a linear controlled discrete-time fractional-order system, as defined by $$\left\{ \begin{array}{ccc}\Delta ^{\gamma }x_{k+1} & = & Ax_{k}+B \Delta ^{\beta }u_{k} \\ x_{0} & = & x_{0}%\end{array}%\right. $$The corresponding output, denoted as $y_{k} = Cx_{k}$, is intended to be stable, i.e., $\underset{k\rightarrow \infty }{\lim} y_k=0 $. More precisely, we suppose the existence of a fractional feedback control denoted as  $\Delta ^{\beta }u_{k}=\Delta^{\beta }Lx_{k}$, where the matrices $A$, $B$, $C$, and $L$ are suitably chosen. The characterization of the maximal output set $\Upsilon \left( \mathcal{R} \right)$ is investigated by defining the fractional derivative in the Grunwald-Letnikov sense. Specifically, $ \Upsilon \left( \mathcal{R} \right) =\left\{ x_{0}\in \mathbb{R} ^{n}/ y_{k} \in \mathcal{R},\text{ }\forall k\geq 0 \right\} $ where $\mathcal{R}$ $ \subset $ $\mathbb{R}^n$ represents a constraint set. It can be shown, through the use of stability and observability hypotheses, that a finite number of inequations can derive $ \Upsilon \left( \mathcal{R} \right)$. The maximal output set is determined using an advanced algorithmic approach. In order to clarify the theoretical results, relevant algorithms and numerical simulations have been included.