| Controllability, Observability and Stability for a Class of Fractional-Order Linear Time-Invariant Control Systems |
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| 作者姓名： | 曾庆山 曹广益 朱新坚 |
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| 作者单位： | Dept. of Automation，Dept. of Automation，Dept. of Automation Shanghai Jiaotong Univ.，Shanghai 200030，China，Shanghai Jiaotong Univ.，Shanghai 200030，China，Shanghai Jiaotong Univ.，Shanghai 200030，China |
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| 基金项目： | Shanghai Science and Technology Devel-opm ent Funds ( No.0 1160 70 3 3) |
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| 摘 要： | IntroductionThe concepts of controllability and observabil-ity,introduced by Kalman1] ,are of extreme im-portance in control theory and engineering. Thereal objects are generally fractional2 ] ,however,the control systems used so far are all consideredas integer- order systems.Disregarding the real or-der of the systems was caused mainly by the com-plexity and the absence of adequate mathematicaltools.The fractional calculus theory was devel-oped by a lotof mathematicians and the applicatio…
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| 关 键 词： | 稳定性 控制不变性 偏微分算法 可观测性 控制论 |
Controllability,Observability and Stability for a Class of Fractional-Order Linear Time-Invariant Control Systems |
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| ZENG Qing-shan,CAO Guang-yi,ZHU Xin-jian.Controllability, Observability and Stability for a Class of Fractional-Order Linear Time-Invariant Control Systems[J].Journal of Shanghai Jiaotong university,2004,9(2):20-24. |
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| Authors: | ZENG Qing-shan CAO Guang-yi ZHU Xin-jian |
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| Institution: | Dept.of Automaion,Shanghai Jiaotong Univ.,Shangai 20030,China |
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| Abstract: | The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov's stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems. |
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| Keywords: | fractional calculus fractional-order linear time-invariant systems controllability observability stability |
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