分数阶离散线性系统的最大输出集

Q3 Mathematics
A. El Bhih, Y. Benfatah, A. Ghazaoui, M. Rachik
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引用次数: 2

摘要

本文考虑一个由\[\Delta ^{\alpha }x_ {k+1}=Ax_k+B u_k, \quad k \geq 0, \quad x_{0} \in \mathbb{R}^{n};\]、\[y_{k}=Cx_k, \quad k \geq 0,\]定义的线性离散分数阶系统,其中$A$、$B$和$C$为适当矩阵,$x_{0}$为初始状态,$\alpha$为导数阶数,$y_k$为信号输出,$u_k=K x_k$为反馈控制。通过定义Grunwald-Letnikov意义上的分数阶导数,我们研究了最大输出集$\Gamma(\Omega)=\lbrace x_{0} \in \mathbb{R}^{n}/y_{i} \in \Omega,\forall i \geq 0 \rbrace$的特征,其中$\Omega\subset\mathbb{R}^{p}$是约束集;并利用稳定性和可观测性的一些假设,证明了$\Gamma(\Omega)$可以由有限个不等式导出。提出了一种识别最大输出集的有效算法;并给出了相应的算法和数值模拟来验证理论结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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, $\Gamma(\Omega)=\lbrace x_{0} \in \mathbb{R}^{n}/y_{i} \in \Omega,\forall i \geq 0 \rbrace$, 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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来源期刊
Mathematical Modeling and Computing
Mathematical Modeling and Computing Computer Science-Computational Theory and Mathematics
CiteScore
1.60
自引率
0.00%
发文量
54
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