Adaptive delay-dependent synchronization of nonlinear time delay systems

This document explores the synchronization problem for two nonlinear time-delay chaotic master-slave systems having unidentified parameters. The state dynamics of the slave system are also corrupted by the disturbance. An adaptive controller is proposed for synchronization of the two systems and the adaptation laws are derived for the estimation of unknown parameters. A delay-dependent condition in the form of LMI is derived so that the controller can be constructed. Lyapunov-Krasovskii functional is used to verify the stability of the master-slave system with proposed controller and the L₂ gain from disturbance to the synchronization error is proved to be bounded. The nonlinearity without delay is handled in an exclusively rare manner for the case of time-delay systems by making an adaptive scheme. A demonstrative numerical problem is discussed to illustrate the practicality of the projected approach.