Feedback control and hybrid projective synchronization of a fractional-order Newton–Leipnik system

In this work, stability analysis of the fractional-order Newton–Leipnik system is studied by using the fractional Routh–Hurwitz criteria. The fractional Routh–Hurwitz conditions are used to control chaos in the proposed fractional-order system to its equilibria. Based on the fractional Routh–Hurwitz conditions and using specific choice of linear feedback controllers, it is shown that the Newton–Leipnik system is controlled to its equilibrium points. Moreover, the theoretical basis of hybird projective synchronization of commensurate and incommensurate fractional-order Newton–Leipnik systems is investigated. Based on the stability theorems of fractional-order systems, the controllers for hybrid projective synchroniztion are derived. Numerical results show the effectiveness of the theoretical analysis.

► In this paper, We are going to use the fractional Routh-Hurwitz conditions to study the stability conditions in the fractional-order Newton-Leipnik system.
► Conditions for linear feedback control are obtained as well.
► And the hybrid projective synchronization of two identical fractional-order Newton–Leipnik systems is achieved.
► The effect of fractional order on chaos control and synchronization is shown.