分数阶奇异系统容许性的充分必要条件

余瑶; 焦壮; 孙长银

doi:10.3724/SP.J.1004.2013.02160

分数阶奇异系统容许性的充分必要条件

doi: 10.3724/SP.J.1004.2013.02160

余瑶^1,2,
焦壮³,
孙长银^1,2,

1.
北京科技大学自动化学院北京 100083;
2.
北京科技大学钢铁流程先进控制教育部重点实验室北京 100083;
3.
北京电子工程总体研究所北京 100854

计量
- 文章访问数: 1908
- HTML全文浏览量: 88
- PDF下载量: 1822
- 被引次数: 0
出版历程
- 收稿日期: 2012-12-12
- 修回日期: 2013-05-13
- 刊出日期: 2013-12-20

Sufficient and Necessary Condition of Admissibility for Fractional-order Singular System

YU Yao^1,2,
JIAO Zhuang³,
SUN Chang-Yin^{1,2
,}

1.
School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
2.
Key Laboratory of Advanced Control of Iron and Steel Process, Ministry of Education, Beijing 100083, China;
3.
Beijing Institute of Electronic System Engineering, Beijing 100854, China

Funds:

Supported by National Outstanding Youth Science Foundation (61125306), Major Research Plan of National Natural Science Foundation of China (91016004), National Natural Science Foun-dation (61203071), Fundamental Research Funds for the Central Universities (FRF-TP-13-017A), and Specialized Research Fund for the Doctoral Program of Higher Education (20130006120027, 20110092110020)

More Information

Corresponding author: SUN Chang-Yin

摘要

摘要: 探讨了阶数在（0，1）区间的分数阶奇异系统的容许性条件. 文中首先给出了正则性，无脉冲性和容许性的定义，然后给出了分数阶奇异系统容许性的充分必要条件，最后通过数值仿真的例子来说明我们给出的容许性条件.
- 分数阶奇异系统 /
- 正则性 /
- 无脉冲性 /
- 容许性
Abstract: This paper focuses on the admissibility condition for fractional-order singular system with order α∈(0, 1). The definitions of regularity, impulse-free and admissibility are given first, then a sufficient and necessary condition of admissibility for fractional-order singular system is established. A numerical example is included to illustrate the proposed condition.
- Fractional-order singular systems /
- regularity /
- impulse-free /
- admissibility

HTML全文

参考文献(29)

[1]	Oldham K B, Spanier J. The Fractional Calculus. New York and London: Academic Press, 1974. 69-83
[2]	Podlubny I. Fractional Differential Equations. New York: Academic Press, 1999. 38-52
[3]	Ichise M, Nagayanagi Y, Kojima T. An analog simulation of non-integer order transfer functions for analysis of electrode processes. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 1971, 33(2): 253-265
[4]	McAdams E T, Lackermeier A, McLaughlin J A, Macken D, Jossinet J. The linear and non-linear electrical properties of the electrode-electrolyte interface. Biosensors and Bioelectronics, 1995, 10(1-2): 67-74
[5]	Gaul L, Klein P, Kemple S. Damping description involving fractional operators. Mechanical Systems and Signal Processing, 1991, 5(2): 81-88
[6]	Makris N, Constantinou M C. Fractional-derivative Maxwell model for viscous dampers. Journal of Structural Engineering, 1991, 117(9): 2708-2724
[7]	Bagley R L, Calico R A. Fractional order state equations for the control of viscoelastically damped structures. Journal of Guidance, Control, and Dynamics, 1991, 14(2): 304-311
[8]	Clerc J P, Tremblay A M S, Albinet G, Mitescu C D. a.c. response of fractal networks. Journal de Physique Letters, 1984, 45: 913-924
[9]	Gao Xin, Yu Jue-Bang. Synchronization of two coupled fractional-order chaotic oscillators. Chaos, Solitons and Fractals, 2005, 26(1): 141-145
[10]	Monje C A, Chen Y Q, Vinagre B M, Xue D Y, Feliu-Batlle V. Fractional-order Systems and Controls: Fundamentals and Applications. London: Springer-Verlag, 2010. 37-78
[11]	Gao Zhe, Liao Xiao-Zhong. A stability criterion for linear fractional order systems in frequency domain. Acta Automatica Sinica, 2011, 37(11): 1387-1394 (in Chinese)
[12]	Guo T L. Controllability and observability of impulsive fractional linear time-invariant system. Computers & Mathematics with Applications, 2012, 64(10): 3171-3182
[13]	Podlubny I. Fractional-order systems and PIλ Dμ controllers. IEEE Transactions on Automatic Control, 1999, 44(1): 208-214
[14]	Oustaloup A, Mathieu B, Lanusse P. The CRONE control of resonant plants: application to a flexible transmission. European Journal of Control, 1995, 1: 113-121
[15]	Ahn H S, Chen Y Q. Necessary and sufficient stability condition of fractional-order interval linear systems. Automatica, 2008, 44(11): 2985-2988
[16]	Lu J G, Chen G R. Robust stability and stabilization of fractional-order interval systems: an LMI approach. IEEE Transactions on Automatic Control, 2009, 54(6): 1294-1299
[17]	Lu J G, Chen Y Q. Robust stability and stabilization of fractional-order interval systems with the fractional order α: the 0 IEEE Transactions on Automatic Control, 2010, 55(1): 152-158
[18]	Hwang C, Cheng Y C. A numerical algorithm for stability testing of fractional delay systems. Automatica, 2006, 42(5): 825-831
[19]	Gao Z, Liao X Z. Robust stability criterion of fractional-order functions for interval fractional-order systems. IET Control Theory and Applications, 2013, 7(1): 60-67
[20]	Ding Y S, Wang Z D, Ye H P. Optimal control of a fractional-order HIV-immune system with memory. IEEE Transactions on Control Systems Technology, 2012, 20(3): 763-769
[21]	Zhu Cheng-Xiang, Zou Yun. Simultaneous identification of fractional-order system structure and order and parameters based on alternately transforming condensed information matrix. Acta Automatica Sinica, 2012, 38(8): 1280-1287 (in Chinese)
[22]	Gabano J D, Poinot T, Kanoun H. Identification of a thermal system using continuous linear parameter-varying fractional modelling. IET Control Theory and Applications, 2011, 5(7): 889-899
[23]	Jin Y, Chen Y Q, Xue D Y. Time-constant robust analysis of a fractional order[proportional derivative] controller. IET Control Theory and Applications, 2011, 5(1): 164-172
[24]	Gao Zhe, Liao Xiao-Zhong. Robust stability criteria for interval fractional-order systems: the 0 Acta Automatica Sinica, 2012, 38(2): 175-182 (in Chinese)
[25]	Dai L Y. Singular Control Systems. Berlin: Springer-Verlag, 1989. 79-98
[26]	Lewis F L. A survey of linear singular systems. Circuits, Systems and Signal Processing, 1986, 5(1): 3-36
[27]	Fang C H, Chang F R. Analysis of stability robustness for generalized state-space systems with structured perturbations. Systems and Control Letters, 1993, 21(2): 109-114
[28]	Fang C H, Lee L, Chang F R. Robust control analysis and design for discrete-time singular systems. Automatica, 1994, 30(11): 1741-1750
[29]	N'Doye I, Zasadzinski M, Darouach M, Radhy N E. Regularization and stabilization of singular fractional-order systems. In: Proceedings of the 4th IFAC Workshop Fractional Differentiation and its Applications. Badajoz, Spain: IFAC, 2010. 145-149