Parameter identification of first order time-delay chaotic system

It' s of vital importance to estimate the unknown parameters of chaotic systems in chaos control and synchronization. Nonlinear observer is used to investigate the problem of parameter identification for two different types of time-delay chaotic systems. The unknown parameter is regarded as the unknown state of the chaotic system. Based on the theory of nonlinear state observer, by selecting suitable nonlinear gain function in observer, which makes the closed-loop error system globally exponentially stable or approximately stable, a sufficient condition for existence of parameter estimator is presented. A numerical simulation on the well-known time-delay logistic system is conducted. Simulation results show that the proposed method is effective for parameter estimation of the time-delay chaotic system.