Disturbed chaotic system synchronization via nonlinear robust interval state observers

Abstract

In this paper, a nonlinear interval state observer design method is synthesized for chaos synchronization between master (drive) and slave (response) systems based on the Luenberger-type observer. The stability study, analyzed with Lyapunov’s approach, is formulated in terms of linear matrix inequalities (LMIs) and subsequently to calculate the observation gain matrix. The stability of the designed state observer is analyzed within the Lyapunov approach and the LMI paradigm. Moreover, the nonlinear interval observer, comprising the lower and upper bound state observers, is used for the state reconstruction of nonlinear perturbed chaotic sys- tems subject to unknown but bounded external disturbances. The effi- ciency and high performances of the aforementioned state observer-based synchronization technique are demonstrated by a large study of numeri- cal simulation for the state synchronization of perturbed unified chaotic systems. keywords : State synchronization Nonlinear perturbed chaotic sys- tems Nonlinear interval observer Lyapunov approach LMI paradigm