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 .
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.
出处
《控制理论与应用》
EI
CAS
CSCD
北大核心
2004年第6期922-926,共5页
Control Theory & Applications
基金
8 63基金项目 (2 0 0 3AA5 170 2 0 )
上海市科技发展基金项目 (0 1160 70 3 3 )
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
fractional order systems
linear time-invariant
stability criteria
Nyquist path
Bode plots
