Hi Rod,
Sure, here is short about Piwik. It's a great solution and can track all kind of things related to site visitors etc.. If you have used Google Analytics before, it's basically the same solution (might be small differences in functionality but overall it is a Google Analytics clone) i.e you can track the same things, it's implementation/tracking is also the same (small javascript script in in html).
Piwik has one important feature that Google analytics don't, you get full data access i.e you log the data in your own MySQL database. I use Piwik for all our sites (+ for email sendouts to track email opens) and then connect to the MySQL database from different Aware IM applications (external DB connection).
Setting it up (Piwik) is simple and I use it in Amazon AWS (free tier takes you a long way and if you go over the free tier limits you don't pay very much). There is a company providing a Piwik prebuilt instance for AWS so installing it is literaly a press of a button. Here is more information about this prebuilt etc. solution: https://aws.amazon.com/marketplace/pp/B0062Q8G2A .
One note, AWS do not allow remote MySQL out of box so you need to work around that by connecting to the DB via SSH in a program like Navicat and then sync the DB to a local/server DB Aware IM in turn can connect to.
Regarding your scenario, I am not sure what you want to track but if it is application usage, I would probably build it directly into the application instead because doing it in Piwik could be tricky (difficult to automate/differentiate between logged in users) but can probably be done if thought through. Piwik is great for things like websites, email opens (pixel image tracking) and is a very good and advanced solution (and easy to use i.e not high-level in implementation or usage).
If you do some cool stuff or implement Piwik, please share your results.