How to shut down a computer having a particular IP address?

Just to give you an answer based on your question: "Shutting down a pc based on just the ip address is impossible"

You can make it possible by making their desktops or shells available over the network. RDP(windows) / SSH or VNC (linux) will do.

Use out-of-band cards (if the computers don't already have them).

They're not cheap cards, but you assign an IP address to each card and you can remotely power cycle/connect/kvm anything really.

Windows has the shutdown /m \\computername command built in, but for Linux you probably would have to install ssh and use ssh root@computername /sbin/shutdown. Why wouldn't a Linux box have SSH installed, anyway?