A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 5 Issue 2
Mar.  2018

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Xuefeng Zhang, "Relationship Between Integer Order Systems and Fractional Order Systems and Its Two Applications," IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 639-643, Mar. 2018. doi: 10.1109/JAS.2016.7510205
 Citation: Xuefeng Zhang, "Relationship Between Integer Order Systems and Fractional Order Systems and Its Two Applications," IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 639-643, Mar. 2018.

# Relationship Between Integer Order Systems and Fractional Order Systems and Its Two Applications

##### doi: 10.1109/JAS.2016.7510205
• Existence of periodic solutions and stability of fractional order dynamic systems are two important and difficult issues in fractional order systems (FOS) field. In this paper, the relationship between integer order systems (IOS) and fractional order systems is discussed. A new proof method based on the above involved relationship for the non existence of periodic solutions of rational fractional order linear time invariant systems is derived. Rational fractional order linear time invariant autonomous system is proved to be equivalent to an integer order linear time invariant non-autonomous system. It is further proved that stability of a fractional order linear time invariant autonomous system is equivalent to the stability of another corresponding integer order linear time invariant autonomous system. The examples and state figures are given to illustrate the effects of conclusion derived.

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