Abstract The ultimate proof of our understanding of nature and engineering systems is reflected in our ability to control them. Since fractional calculus is more universal, we bring attention to the controllability of fractional order systems. First, we extend the conventional controllability theorem to the fractional domain. Strictly mathematical analysis and proof are presented. Because Chua's circuit is a typical representative of nonlinear circuits, we study the controllability of the fractional order Chua's circuit in detail using the presented theorem. Numerical simulations and theoretical analysis are both presented, which are in agreement with each other.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 51109180 and 51479173), the Fundamental Research Funds for the Central Universities, China (Grant No. 201304030577), the Northwest A&F University Foundation, China (Grant No. 2013BSJJ095), and the Scientific Research Foundation on Water Engineering of Shaanxi Province, China (Grant No. 2013slkj-12).
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