| Research on the stability, controllability and observability for fractional order LTI systems |
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| 作者姓名： | 王振滨 曹广益 朱新坚 |
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| 作者单位： | Shanghai Electric Group Co. Ltd Central Academe Shanghai 200023 China，Dept. of Automation Fuel Cell Institute Shanghai Jiaotong University Shanghai 200030，China，Dept. of Automation Fuel Cell Institute Shanghai Jiaotong University Shanghai 200030，China，Dept. of Automation Fuel Cell Institute Shanghai Jiaotong University Shanghai 200030，China |
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| 基金项目： | stability, coSponsored by the National High Technology Research and Development Program of China (Grant No.2003AA517020), the National Natural Science Foundation of China (Grant No.50206012), and Developing Fund of Shanghai Science Committee (Grant No.011607033). |
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| 摘 要： | Fractional calculus has a history of300years.Itoccurred at almost the same time as classical integer or-der calculus,but it is different from the latter.It is asubject studying the derivatives and integrals with arbi-trary order.Since the computation of fractional calculusis much more complicated than that of integer order cal-culus,the development of the theory of fractional calcu-lus mainly focused on the pure mathematical domain formany years,and it is interesting mainly to mathemati-cians.…
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| 关 键 词： | 分数阶系统 LTI 可控性 可观察性 稳定性 |
| 文章编号： | 1005-9113（2006）05-0580-04 |
| 收稿时间： | 2003-11-28 |
Research on the stability, controllability and observability for fractional order LTI systems |
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| WANG Zhen-bin,CAO Guang-yi,ZHU Xin-jian.Research on the stability, controllability and observability for fractional order LTI systems[J].Journal of Harbin Institute of Technology,2006,13(5):580-583. |
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| Authors: | WANG Zhen-bin CAO Guang-yi ZHU Xin-jian |
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| Abstract: | The state space representations of fractional order linear time-invariant(LTI) systems are introduced, and their solution formulas are deduced by means of Laplace transform. The stability condition of fractional order LTI systems is given, and its proof is deduced by means of using linear non-singularity transform and the derivative property of Mittag-Leffler function. The controllability condition of fractional order LTI systems is given, and its proof is deduced by means of using its characteristic polynomial and the Cayley-Hamilton theorem. The observability condition of fractional order LTI systems is given, and its proof is deduced by means of their solution formulas. Finally an example is given to prove the correctness of the stability, controllability, and observability conditions mentioned above.s are deduced by means of Laplace transform. Their stability, controllability and observability conditions are given as well as their proofs. |
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| Keywords: | fractional calculus fractional order system stability controllability observability |
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