assuming that you have ZD1100 series controller... if answer is yes, then last version to use on this controller is 9.10
to use 9.13 controller, you need to have controller ZD1205
yes you can upgrade to 9.13 with ZD3000 however there are multiple upgrades to reach from 9.7 to 9.13... please read all release notes to find out correct upgrade path and also find out what would happen to your exisiting AP's if any... better you contact Support for more info...