Convergence of semi-gradient TD(0) with non-linear function approximation

I am looking for a result that shows the convergence of semi-gradient TD(0) algorithm with non-linear function approximation for on-policy prediction. Specifically, the update equation is given by (borrowing notation from Sutton and Barto (2018))

$$\mathbf w \leftarrow \mathbf w +\alpha [R + \gamma \hat v(S', \mathbf w) - \hat v(S, \mathbf w)] \nabla \hat v(S, \mathbf w)$$

where $$\hat v(S, \mathbf w)$$ is the approximate value function parameterized by $$\mathbf w$$.

Sutton and Barto (2018) mention that the above update equation converges when $$\hat v$$ is linear in $$\mathbf w$$. But I couldn't find a similar result for non-linear function approximation. Any help would be greatly appreciated.