| 分数阶线性定常系统的稳定性及其判据 |
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| 引用本文： | 王振滨,曹广益,朱新坚.分数阶线性定常系统的稳定性及其判据[J].控制理论与应用,2004,21(6):922-926. |
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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： | 上海交通大学,自动化系,上海,200030 |
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| 基金项目： | 863基金项目 (2003AA517020); 上海市科技发展基金项目 (011607033) |
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| 摘 要： | 介绍了分数阶微分方程和分数阶系统 ,给出分数阶线性定常系统的传递函数描述和状态空间描述 .给出了分数阶线性定常系统的稳定性条件 ,并结合分数阶状态方程给出定理的证明 .直接从复分析中的辐角原理出发 ,推导出分数阶线性定常系统 2个有效的稳定性判据 :分数阶系统奈奎斯特判据和分数阶系统对数频率判据 .通过实例验证了其有效性
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| 关 键 词： | 分数阶系统 线性定常 稳定性判据 奈奎斯特路径 波德图 |
| 文章编号： | 1000-8152(2004)06-0922-05 |
Stability conditions and criteria for fractional order linear time-invariant systems |
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| WANG Zhen-bin,CAO Guang-yi,ZHU Xin-jian.Stability conditions and criteria for fractional order linear time-invariant systems[J].Control Theory & Applications,2004,21(6):922-926. |
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| Authors: | WANG Zhen-bin CAO Guang-yi ZHU Xin-jian |
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| Affiliation: | Department of Automation,Shanghai Jiao Tong University,Shanghai 200030,China |
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| Abstract: | The fractional order differential equations and the fractional order linear time-invariant systems are introduced,and their transfer function representation and state-space representation are given.The stability conditions are proposed for the fractional order linear time-invariant systems.A proof is also given based on the fractional order state-space equation.Starting directly from the argument principle of complex analysis,two efficient stability criteria are deduced for fractional order linear time-invariant systems: Nyquist criterion of fractional systems and logarithmic-frequency criterion of fractional systems.An example verifies the effectiveness of the criteria aforementioned. |
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| Keywords: | fractional order systems linear time-invariant stability criteria Nyquist path Bode plots |
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