On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems

Benfatah, Youssef; Bhih, Amine El; Rachik, Mostafa; Tridane, Abdessamad

doi:10.1007/s12555-020-0486-6

Cited by 4 publications

(1 citation statement)

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“…In [25], the authors have considered the infinite dimensional linear systems and they have characterized the set of all gain operators making the system insensitive to the influence of uncertain initial state. Additional references that provide information on the investigation of the maximal output set are included in [26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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

Bhih¹,

Benfatah²,

Ghazaoui³

et al. 2022

Math. Model. Comput.

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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, $\Gamma(\Omega)=\lbrace x_{0} \in \mathbb{R}^{n}/y_{i} \in \Omega,\forall i \geq 0 \rbrace$, where $\Omega\subset\mathbb{R}^{p}$ is a constraint set; and, by using some hypotheses of stability and observability, we prove that $\Gamma(\Omega)$ can be derived from a finite number of inequations. A powerful algorithm approach is included to identify the maximal output set; also, some appropriate algorithms and numerical simulations are given to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 99%