Robust sliding-mode backstepping design for synchronization control of cross-strict feedback hyperchaotic systems with unmatched uncertainties

► Make most synchronization errors to zero under unmatched uncertainties. ► How to realize synchronization using only two controls. ► Can be applied to a variety of chaotic systems by using modified Sontag-formula. This paper is concerned with the synchronization problem for a class of hyperchaotic chaotic systems. Using sliding mode control approach and backstepping control, a robust control scheme is proposed to make most of the synchronization errors of the systems to zero for matched and unmatched uncertainties. And only one of the synchronization errors of the systems may not be zero, but it is bounded. Meanwhile, the chattering phenomenon is eliminated. The proposed methods can be applied to a variety of chaos systems which can be described by the so-called cross-strict feedback form. Numerical simulations are given to demonstrate the efficiency of the proposed control schemes.