A new scheme to synchronize chaotic discrete-time systems via a scalar signal

Chaos synchronization is an important research topic in the field of nonlinear circuits and systems. This paper presents a new synchronization scheme, where two chaotic discrete-time systems synchronize for any invertible scaling matrix. Specifically, potentially different linear combinations of response system states synchronize with each drive system state. The proposed observer-based approach presents some useful features: i) it enables exact synchronization to be achieved in finite time; ii) it exploits a scalar synchronizing signal; and iii) it can be applied to a wide class of discrete-time chaotic (hyperchaotic) systems. An example is reported, which shows that exact synchronization is effectively achieved in finite time, for two arbitrary scaling matrix, via a scalar synchronizing signal only.