discrete-time system

On the maximal output set of fractional-order discrete-time linear systems

In this paper, we consider a linear discrete-time fractional-order system defined by \[\Delta ^{\alpha }x_ {k+1}=Ax_k+B u_k, \quad k \geq 0, \quad x_{0} \in \mathbb{R}^{n};\] \[y_{k}=Cx_k, \quad k \geq 0,\] where $A$, $B$ and $C$ are appropriate matrices, $x_{0}$ is the initial state, $\alpha$ is the order of the derivative, $y_k$ is the signal output and $u_k=K x_k$ is feedback control.  By defining the fractional derivative in the Grunwald–Letnikov sense, we investigate the characterization of the maximal output set, $\Gamma(\Omega)=\lbrace x_{0} \in \mathbb{R}^{n}/y_

Identifying the set of all admissible disturbances: discrete-time systems with perturbed gain matrix

This paper focuses on linear controlled discrete-time systems which subject to the control input disturbances.  A disturbance is said to be admissible if the associated output function verifies the output constraints.  In this paper, we address the following problem: determine the set of all admissible disturbances from all disturbances susceptible to the deformation of control input.  An algorithm for computing the maximum admissible disturbances set is described and the sufficient conditions for finite termination of this algorithm are given.