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.
['Bin Liu', 'David J. Hill', 'Jian Yao']
Global Uniform Synchronization With Estimated Error Under Transmission Channel Noise