Stabilization of a new commensurate/incommensurate fractional order chaotic system

Abstract

In the current article, agreeing on the stability theory of fractional order systems, the conditions for the asymptotic stability of nonlinear fractional order systems are presented. We discuss the stabilization of new fractional order chaotic system where the state equations contain the same or different fractional orders. Then we design a control strategy for stabilization of new fractional order chaotic system. Our aim is to stabilize the unstable equilibrium points of fractional order chaotic systems by planning a fit linear state feedback controller. In the following, a comparison between linear state feedback controller and sliding mode control for commensurate and incommensurate new fractional order chaotic systems is conducted. Numerical simulations approve the validity of the presented results.