Dead-beat synchronization control in discrete-time chaotic systems

Referring to chaos synchronization, it can be noticed the lack of a general approach enabling 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. This paper focuses on discrete-time systems, while the companion paper [1] deals with continuous-time systems. Herein, the observer-based synchronization framework exploits a structural condition related to the controllability matrix of the error system in order to achieve any type of dead-beat synchronization (i.e., exact synchronization in finite time) via a scalar synchronizing signal. Examples of different types of synchronization are illustrated, with the aim to show the capabilities of the conceived approach.