Stability for nonlinear fractional order systems: an indirect approach
Stability for nonlinear fractional order systems: an indirect approach
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非线性分数阶系统的稳定性：一种间接方法
DOI：
10.1007/s11071-017-3497-y
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发表时间：
2017
影响因子：
5.6
通讯作者：
Yong Wang
中科院分区：
文献类型：
--
作者：
Yuquan Chen;Yiheng Wei;Xi Zhou;Yong Wang
本文首先证明了采用Caputo导数或Riemann-Liouville导数的分数阶系统可以表示为具有适当初值配置的连续频率分布模型。然后，讨论了分数阶系统与其对应的整数阶系统的稳定性之间的关系，证明了在适当的条件下，整数阶系统的稳定性蕴涵着分数阶系统的稳定性。此外，由于分数阶系统总是通过逼近来实现，因此我们将稳定性定理扩展到有限维情况。最后给出了一些例子来说明所提出的稳定性定理的使用和有效性。
In this paper, we first verify that fractional order systems using Caputo’s or Riemann–Liouville’s derivative can be represented by the continuous frequency distributed model with initial value carefully allocated. Then, the relation of the stability between the fractional order system and its corresponding integer order system is discussed and it is proven that stability of integer order system implies the stability of its corresponding fractional order system under some mild conditions. Moreover, we extend the stability theorems to the finite-dimensional case since fractional order systems are always implemented by approximation. Some illustrative examples are finally provided to show the usage and effectiveness of the proposed stability theorems.