Finite-time projective synchronization control of variable-order fractional chaotic systems via sliding mode approach

This brief intends to tackle the problem of finite-time projective synchronization of variable-order fractional (VOF) chaotic systems through sliding mode control (SMC) method. Firstly, for the VOF unperturbed chaotic systems, the novel VOF integral- and derivative-type sliding surface have been designed with the aid of the theory of VOF calculus, respectively. Secondly, the VOF control strategies are proposed which rely on the corresponding sliding surface to guarantee the projective error systems to be asymptotically stable in finite-time. Furthermore, by utilizing two transformations of VOF calculus, a novel finite-time stability criterion is also obtained, i.e., the upper boundary of reaching time is derived. In the end, a numerical study is taken to illustrate the superiority of the proposed method