LaSalle's invariance principle for positive semi definite V

Question

With $\dot{\textbf{x}}=\dot{\textbf{x}}(\textbf{x})$, if I have a function which has $V(\textbf{x})>0$ when $\textbf{x}\neq \textbf{0}$ for some domain of x, and if $\dot{V}(\textbf{x})\leq 0$ for all $\textbf{x}$, can I somehow apply LaSalle's invariance principle? More specifically, my issue is that my $V(\textbf{x})$ is positive definite in only some variables in $\textbf{x}$, with some other variables in $\textbf{x}$ not being considered.