Generalized Projective Synchronization for the Horizontal Platform Systems via an Integral-type Sliding Mode Control

Abstract

In this paper, an integral-type sliding mode controller design for generalized projective synchronization of two horizontal platform systems (HPS) is considered. The concept of extend systems is used such that continuous control input is obtained using a sliding mode design scheme. Based on the Lyapunov stability theorem, control laws are derived. It is guaranteed that under the proposed control law, an uncertain slave chaotic HPS can asymptotically track a master chaotic HPS. The converging speed of error states can be arbitrarily set by assigning the corresponding dynamics to the sliding surfaces. Numerical simulations are shown to verify the results and this control law can be applied to another chaotic system of the same design scheme.