Abstract
This paper presents new synchronization results for a class of nonlinear discrete-time chaotic systems based on a synergetic observer design with a circuit implementation. The synchronization master–slave method adopted is based on the synergetic theory which is exploited to propose a synergetic observer. The system (master) adopted is that of the discrete-time Lur’e forms. One of the main contributions of this paper is to exploit this simple special form as master in order to design a synergetic observer (slave) which allows us to control the rate of convergence of the synchronization error using the synergetic design parameter matrix. In order to achieve the synchronization method, sufficient conditions for asymptotic synchronization are given. Two simulation examples are provided to show the effectiveness of the method in two different cases: the master system respects and does not respect the Lur’e form. Furthermore, experimental implementation results using Arduino boards are illustrated to validate the proposed approach.