Knowing that you are fond of classical music, I'd like to invite you to join me and welcome you to show your performance. （正）

Having known that you are fond of classical music, I'd like to invite you to join me and welcome you to show your performance. （？）

如果两个动作在同一个时间内发生，know 最好使用一般体：knowing。如果两个动作先后发生，为了明确 know早于另外一个动作，使用完成体：having known。例如：

He did it on purpose, knowing it would annoy her.
他明知会激怒她，却故意那么做。
《牛津词典》
Having known the truth, the grocer gave up the prosecution.
知道真相后，食品商放弃了起诉。