An Alternative Admissibility Theorem for Singular Fractional Order Systems
An Alternative Admissibility Theorem for Singular Fractional Order Systems
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DOI：
10.1109/access.2019.2938587
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发表时间：
2019-08
期刊：
影响因子：
3.9
通讯作者：
Xuefeng Zhang;Zeli Zhao;Li Li-Li
中科院分区：
文献类型：
--
作者：
Xuefeng Zhang;Zeli Zhao;Li Li-Li
本文研究了分数阶为1的奇异分数阶系统的可容许性问题。首先，给出了一个容许等价定理，建立了奇异FOS与相应的整数阶系统之间的桥梁。然后，一个替代的必要和充分条件，奇异FOS不同于现有的结果。该判据将奇异矩阵E包含在矩阵不等式中，能更好地处理具有不确定矩阵E的广义系统的镇定问题。此外，建立了奇异FOS的广义李雅普诺夫方程，该方程等价于所提出的替代容许性准则。最后，通过两个数值例子说明了本文主要结果的有效性。
This work is concerned with the issue of admissibility for singular fractional order systems (FOS) with the fractional order $1\leq \alpha . Firstly, an admissibility equivalence theorem is presented to establish a bridge between singular FOS and corresponding integer order systems. Then, an alternative necessary and sufficient condition for singular FOS different from existing results is developed. In this new criterion, singular matrix $E$ is included in matrix inequality, which can better deal with the issue of stabilization for singular systems with uncertainty matrix $E$ . Moreover, generalized Lyapunov equation of singular FOS is established, which is equivalent to the proposed alternative admissibility criterion. Finally, two numerical examples are presented to illustrate the effectiveness of main results in this paper.