An algebraic observability approach to chaos synchronization by sliding differentiators

In this paper, an observability approach to the synchronization of chaotic and hyperchaotic systems is presented. The proposed method allows the reconstruction of a chaotic attractor from a scalar observable and its derivatives. The method is based on the concept of algebraic observability; hence, it is directly applicable to all chaotic algebraic systems. Moreover, it is shown that a sliding differentiator, derived by a second-order suboptimal control algorithm, can be used to reconstruct the time derivatives of the observable. This makes it possible to estimate the system state, i.e., chaos synchronization, in a finite time.