Robust synchronization of chaotic horizontal platform systems with phase difference

This paper studies a robust synchronization of non-autonomous chaotic systems with parameter mismatch. In the synchronization scheme, a linear state error feedback control is used to couple the master and slave horizontal platform systems excited by harmonic external forces, between which there exists a phase mismatch. A new definition of global synchronization with error bound is introduced. Using Lyapunov's stability theory, the sufficient synchronization criteria for the scheme are proven and the corresponding synchronization error bound is estimated. The synchronization criteria are further optimized by optimally designing a quadratic Lyapunov function to more precisely estimate the synchronization error bound. The illustrative simulations verify the effectiveness of these criteria. The estimated synchronization error bound is compared with numerical one in the examples.