Definitions
Persistence Excitation on page 121 here or shortly here and here. A signal is PE if this limit exists $r_u(\tau)=\lim_{N\rightarrow\infty}\frac 1 N \sum_{t=1}^{N} u(t+\tau)u^T(t)$
And it is of order $n$ if some condition for unknown matrix $R_u(\tau)$ is satisfied. I cannot understand this part of the definition, more in comments.
How can the limit exist with the PE? If it does, why is it not always zero with most signals? Could someone open the examples a bit to show the non-zero limits? What is the difference between capital $R$ and small $r$?
Observations