Necessary and Sufficient Conditions for Consensus of Delayed Fractional‐order Systems
Necessary and Sufficient Conditions for Consensus of Delayed Fractional‐order Systems
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DOI：
10.1002/asjc.492
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发表时间：
2012-11
影响因子：
2.4
通讯作者：
Jun Shen;Jinde Cao
中科院分区：
文献类型：
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作者：
Jun Shen;Jinde Cao
本文研究了具有输入时滞的分数阶系统的一致性问题。利用拉普拉斯变换方法，首先讨论了分数阶系统在频域上的稳定性。基于广义Nyquist稳定性判据，进一步导出了具有相同输入时滞的分数阶系统在有向相互作用拓扑上的一致性的充分必要条件。进一步，明确给出了具有异构输入时滞的分数阶系统在交互拓扑为无向时的一致性条件。最后，通过算例说明了理论结果的有效性和优越性。
In this paper, we study the consensus problem of fractional‐order systems with input delays. Using Laplace transform method, the stability of the fractional‐order systems is first discussed in the frequency domain. Based on the generalized Nyquist stability criterion, a necessary and sufficient condition is further derived to ensure the consensus of fractional‐order systems with identical input delays over directed interaction topology. Furthermore, when the interaction topology is undirected, the consensus condition of fractional‐order systems with heterogeneous input delays is explicitly given. Finally, some illustrative examples are presented to show the effectiveness and advantages of the theoretical results.