Robust synchronization with error bound of horizontal platform systems with parameter mismatch

This paper studies robust synchronization of two chaotic horizontal platform systems with external harmonic excitations via linear state error feedback control, where parameter mismatch exists between the external harmonic excitations in the master system and slave one. Based on lyapunov stability theory and sylvesterpsilas criterion, some sufficient synchronization criteria are derived in the form of algebraic inequalities and the corresponding synchronization error bounds are estimated. Besides, we also establish the relationships between the estimated synchronization error bound and parameter mismatch as well as the coupling coefficients. Simulations verify the effectiveness of these criteria, and the estimated synchronization error bounds can be compared with the numerical ones in the examples. Both the theoretical and numerical results show that the present linear state error feedback control is effective and robust.