ABSTRACT
This chapter is devoted to presenting some definitions and relevant results of different techniques of synchronization for both continuous time systems and discrete time systems. In Sec. 6.2, we present the notion of compound synchronization of different chaotic systems. In Sec. 6.3, the synchronization of 3-D continuous-time quadratic systems using a universal non-linear control law is presented. In Sec. 6.4, the notion of co-existence of certain types of synchronization and their inverse is defined with some relevant results. In Sec. 6.5, we present the synchronization of 4-D continuous-time quadratic systems using a universal non-linear control law. In Sec. 6.6, the quasi-synchronization of discrete time systems with different dimensions is presented. Sec. 6.7 is devoted to the chaotification of 3-D linear continuous-time systems using the signum function feedback, giving a very simple chaotic system. As an example of chaos control, we present in Sec. 6.8 the example of controlling a 3-D cancer model with structured uncertainties. For discrete times systems, Sec. 6.9 reveals the technique used for controlling a homoclinic chaotic attractor in the general two-dimensional piecewise smooth map. Sec. 6.10 covers the creation of robust chaos in the general 2-D discrete mappings via the controller of a simple piecewise smooth function under some realizable conditions. Finally, a more general case of chaotifying stable n-D linear maps via the controller of any bounded function is presented and discussed in Sec. 6.11.
