Relationship between integer order systems and fractional order system and its two applications

Existence of periodic solutions and stability of fractional order dynamic systems are two important and difficult issues in fractional order systems U+0028 FOS U+0029 field. In this paper, the relationship between integer order systems U+0028 IOS U+0029 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.