Taking into account an autonomous system (A,, C) (time-invariant system), the kernel of the G is defined as the unobservable subspace of the system (A,, C).
Taking into account an autonomous system (A,, C) (time-invariant system), the observability of this system is equivalent to the injectivity of linear application. Therefore, the kernel of the G application is defined as the unobservable subspace of the system (A,, C).