Do you mean Solanum rantonnetii Royal Robe?

The only solanum I know of - may or may not be helpful to question - is the chilean potato tree which has purple/blue flowers. If it is this then it doesn't like hard frosts and should only be cut down after flowering. Good news is that it will recover with some dead wood - cut it down to new sprouts after all danger of frost is past. I doubt the tree itself is dead unless the frost you mention was particularly severe and penetrated right down the main branch. Wait until spring then remove all dead wood, and prune to shape after flowering.

If S. rantonnetii, as long as the stems are still moist and flexible, it should sprout right back, though it may be a little later in spring before it blooms again, Bertharae.