The shutdown procedure cleanly shuts down the zone.
For more information, see Assigning Limited Rights to Zone Administrators.
global$ zoneadm list -v
You will see a display that is similar to the following:
ID NAME STATUS PATH BRAND IP 0 global running / solaris shared 1 my-zone running /zones/my-zone solaris excl
global$ zoneadm -z my-zone shutdown
global$ zoneadm -z my-zone shutdown -r boot_options
global$ zoneadm list -v