Comments on "Sufficient and Necessary Condition of Admissibility for Fractional Order Singular Systems"
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摘要: 《自动化学报》39卷12期的"分数阶奇异系统容许性的充分必要条件"得到了基于线性矩阵不等式的分数阶广义系统容许性充分必要条件.本文给出一个数值反例表明文献[
1 ]中定理1的充分条件结论并不成立, 必要条件也不准确.最后, 给出了修改正确的分数阶广义系统容许性充分必要条件.相比于文献[1 ]的定理1, 改进后充要条件没有保守性并去除了原文中分数阶广义系统正则性的限制要求.Abstract: In Acta Automatica Sinica Vol. 39 No. 12 "Sufficient and necessary condition of admissibility for fractional-order singular system", it is claimed that the necessary and sufficient condition of the admissibility for fractional order singular systems is given in terms of linear matrix inequalities (LMIs). In this note, a numerical example is presented to show that the sufficient condition of Theorem 1 given in reference [1 ] does not hold and its necessary condition is not accurate. At last, the modified necessary and sufficient condition for the admissibility of the fractional order singular systems is proposed. Compared with Theorem 1 in the reference [1 ], the improved necessary and sufficient condition is not conservative and the restriction of the regularity of the fractional order singular systems in original article is removed.-
Key words:
- Fractional order singular systems /
- stability criteria /
- admissibility /
- linear matrix inequality (LMI)
1) 本文责任编委 孙长银 -
[1] 余瑶, 焦壮, 孙长银.分数阶奇异系统容许性的充分必要条件.自动化学报, 2013, 39(12): 2160-2164 doi: 10.3724/SP.J.1004.2013.02160Yu Yao, Jiao Zhuang, Sun Chang-Yin. Sufficient and necessary condition of admissibility for fractional-order singular system. Acta Automatica Sinica, 2013, 39(12): 2160-2164 doi: 10.3724/SP.J.1004.2013.02160 [2] Matignon D. Stability results for fractional differential equations with applications to control processing. In: Proceedings of the 1996 Computational Engineering in Systems Applications. Lille, France: IEEE-SMC, 1996. 963-968 [3] Marir S, Chadli M, Bouagada D. A novel approach of admissibility for singular linear continuous-time fractional-order systems. International Journal of Control, Automation and Systems, 2017, 15(2): 959-964 doi: 10.1007/s12555-016-0003-0 [4] Liu Y C, Cui L, Duan D P. Dynamic output feedback stabilization of singular fractional-order systems. Mathematical Problems in Engineering, 2016, 2016: Article ID 9694780 [5] Zhang X F. Relationship between integer order systems and fractional order systems and its two applications. IEEE/CAA Journal of Automatica Sinica, 2018, 5(2): 639-643 doi: 10.1109/JAS.2016.7510205 [6] Wang C H, Li H H, Chen Y Q. $H_\infty$ output feedback control of linear time-invariant fractional-order systems over finite frequency range. IEEE/CAA Journal of Automatica Sinica, 2016, 3(3): 304-310 doi: 10.1109/JAS.2016.7508806 -
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