Remote command to exit and restart kodi

Running Kodi 16.1 on Linux Mint Sarah X64.
PC is left running 24/7 but the rest of the home theatre only gets turned on to watch Kodi (mostly live DVB).
Was wondering if there is any way to get the remote to “Exit” Kodi, when shutting down the rest (yes, it does generally do this), but the more important thing is how to get it to start Kodi, when starting up the rest of the home theatre?
Can the “exit” command be setup to Toggle kodi starting from the desktop….
Previously, was using a PC and the shutdown command would put the PC to sleep, then wake it back up.
Thanks.