I was reading an article on Euler-Lagrange systems. It is stated there that since M(q) and C(q,q') depend on q, it is not autonomous. As a result, we cannot use LaSalle's theorem. I have uploaded that page of the article and highlighted the sentence. (ren.pdf)
Then, I read Spong's book on robotics, and he had used LaSalle's theorem. I am confused. (spong.pdf)
I did some research, and found out that non-autonomous means it should not explicitly depend on the independent variable. Isn't independent variable time in these systems? So, shouldn't they be considered autonomous?