Approximate Internal Synchronization by Groups

In this chapter, we will clarify that the independence of approximately synchronizable state by groups with respect to applied controls the non extensibility to other approximate synchronization, the linear independence of the components of the approximately synchronizable state by groups as well as the necessity of the condition of \(C_p\) -compatibility, all these properties are the consequence of the minimality of Kalman’s rank condition. The material in this chapter is mainly taken from [43, 48, 51].