If you are referring only to news, you can use either: "I will update you on the latest developments"  "I will keep you up to date with the latest developments."

If you are talking about workers' skill levels, then you might say: "Our employees' skills need to be updated / need updating - they are not good enough for today's market.  We need to bring their skills up to date."  

1 "to keep oneself/somebody informed about something" This usually refers to a new topic.  When you find out something about this new topic, let the person know.

2 "to keep somebody updated on the latest news"   An update means that info was already given on a topic, but that info could change at any time. Therefore "updates" are required so that everyone can know the latest news on that topic, or keep "up to date" on it.

3 "to keep the staff up to date with the new systems of the company?"  This is the sentence that has a more specific topic.  The topic is the "systems of the company".  Since the sentence uses "up to date", that means the topic is already familiar to them/has been addressed.  Now they need to be briefed on any changes - as the changes happen.

Thank you very much ^^