Without using "have" one could write:
William Shakespeare was known to perform his own plays.
We use "was" rather than "is" because this event is in the past, quite a while in the past in this case.
The form "is known to have" is talking about the current state of knowledge, not the current performances. The use of "have" indicts that the performance are in the past, although it could be the recent past.
David Siegel is known to have made typos on Stack Exchange.
The event is currently known, and is in the past, although in this case the very recent past.