I installed 16.04-LTS via the Ubuntu upgrade procedure, and it works fine.
I installed the DisplayLink USB Graphics Software for Ubuntu, version 1.1.62.
http://displaylink.org/forum/showthread.php?t=64503
I had to disable secureboot in the BIOS. As an alternative it is possible to add a signature to the driver.
Getting the driver to work on the XPS13 is discussed in the thread at the following URL.
http://displaylink.org/forum/showthread.php?t=64527
There is a problem with configuring multiple displays because settings>hardware>displays responds with "could not get screen information".
I googled this problem and generally the suggestions involved invoking the following.
sudo apt-get install --reinstall ubuntu-desktop
This proposal may help accidentally, but after sorting out the various variants of gnome and experimenting, it seems that "settings>hardware>displays" is actually looking for appearance information, which has been removed from settings in the latest version of the gnome desktop configuration system.
If one clicks on the desktop background to get a menu including change desktop background and then clicks on change desktop background, appearance configuration pops up, and then one can choose "all settings" at which point displays works, and one can configure the multiple displays.