In Linux, only the superuser is allowed to shutdown or reboot the system, unless some special settings have been made.

How to shutdown or reboot your Linux station:
The command for shutdown/reboot is called “shutdown” and can be scheduled:
You can ask your computer to shut itself down (or reboot) at 20:00, for example, or in 15 minutes from this moment:
shutdown -r is for restart, and shutdown -h is for power off.
Shutdown or reboot NOW:
$ sudo shutdown -h now
OR $ sudo shutdown -r now
Shutdown or reboot in 10 minutes:
$ sudo shutdown -h +10
OR $ sudo shutdown -r +10
Shutdown or reboot at 20:00 o’clock:
$ sudo shutdown -h 20:00
OR $ sudo shutdown -r 20:00
You can also use the command reboot, halt or poweroff to restart your Linux system.
In Debian/Ubuntu/Linux Mint, halt and poweroff are symbolic links to /sbin/reboot:
$ ls -l /sbin/{halt,poweroff}
lrwxrwxrwx 1 root root 6 2012-05-21 22:38 /sbin/halt -> reboot
lrwxrwxrwx 1 root root 6 2012-05-21 22:38 /sbin/poweroff -> reboot
Be carefull not to be connected on ssh and by mistake shutdown the remote server instead of your local station!!! I recommand using Molly-Guard to protect your system from unwanted shutdowns. Read more about Molly-Guard here.