Chaos synchronisation of continuous systems via scalar signal

Abstract

By analyzing the issue of chaos synchronization in the literature, it can be noticed the lack of a general approach, which would enable any type of synchronization to be achieved. Similarly, there is the lack of a unified method for synchronizing both continuous-time and discrete-time systems via a scalar signal. This paper and the companion one [1] aim to bridge these two gaps by presenting a novel general unified framework to synchronize chaotic systems via a scalar signal. The framework, based on the concept of observer, enables any type of synchronization defined to date to be achieved for both continuous-time and discrete-time systems via a scalar signal. This paper focuses on continuous-time systems, while the companion paper [1] deals with discrete-time systems. Herein, the observer-based framework exploits a structural condition related to the uncontrollable eigenvalues of the error system. Several examples of different types of synchronization are illustrated, with the aim to show the capabilities of the approach.