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

作　　者：王振滨[1] 曹广益[1] 朱新坚[1] 

机构地区：[1]上海交通大学自动化系,上海200030

出　　处：《控制理论与应用》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 )

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.

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 

分 类 号：O172[理学—数学]