"The button" is either system reset or IPL (clear). If there's a way to convey that to the software, it would be cool, but I doubt it.
When you pull the plug there is little left to do the recovery. But we have the #CP SIGNAL SHUTDOWN to tell the Linux virtual machine to get out. You pick it up in /etc/inittab like a ctrl-alt-del and decide to make it reboot or shutdown or what else you like.
Rob
