Master–slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control

Global chaos synchronization of two identical non-autonomous horizontal platform systems coupled by linear state error feedback controller is investigated. The sufficient criteria for global chaos synchronization are deduced based on the stability theory of linear time-varied systems and Lyapunovʹs direct method, of which, the criteria related to general coupling matrix are first proved and applied to derive the ones related to some special coupling matrices. In the examples, the coupling strengths are designed by the obtained criteria and the appearances of chaos synchronization are verified. It is analytically and numerically examined that the synchronization criteria based on Lyapunovʹs direct method are sharper than the criteria based on the stability theory of linear time-varied systems.