Global uniform synchronization with estimated error under transmission channel noise

This paper investigates the problem of estimating synchronization errors and its application to global uniform synchronization with an estimated error bound for the master-slave chaos synchronization scheme via linear control input, which is possibly subject to disturbances by unknown but bounded channel noise and time-delay. Based on Lyapunov function, Razumikhin technique, nonlinear parametric variation, and input-to-state stability (ISS) theory, estimation formulas of synchronization errors with or without time-delays but with noise in transmission channel (TC) are derived. By using the error estimation formula, the maximal upper bound for time-delays is also obtained. These formulas can be used to design a control gain matrix which forces the synchronization error to the minimal value. Meanwhile, theoretical discussion is made by comparing Lyapunov-Krasovskii function method with respect to time-delays in TC. After the theoretical analysis, some representative examples and their numerical simulations are given for illustration.