| 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.[点击复制] |
| WANG Zhen-bin, CAO Guang-yi, ZHU Xin-jian.Stability conditions and criteria for fractional order linear time-invariant systems[J].Control Theory and Technology,2004,21(6):922~926.[点击复制] |
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| 分数阶线性定常系统的稳定性及其判据 |
| Stability conditions and criteria for fractional order linear time-invariant systems |
| 摘要点击 3108 全文点击 2026 |
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| DOI编号 10.7641/j.issn.1000-8152.2004.6.018 |
| 2004,21(6):922-926 |
| 中文关键词 分数阶系统 线性定常 稳定性判据 奈奎斯特路径 波德图 |
| 英文关键词 fractional order systems linear time-invariant stability criteria Nyquist path Bode plots |
| 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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| 中文摘要 |
| 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 |
| 英文摘要 |
| 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. |