Controllability of fractional-order Chua's circuit

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.