Is there a way to power down the linux side from the Leonardo side?

I'd like to be able to power down the linino from the arduino (saving power) then I'd like to turn it back on using a command from the arduino side (to communicate with a WiFi network). The linino would be powered down for 55 minutes out of each hour so I could expect significant energy savings.

Thank you

Sadly, found out that the answer is yes but it won't wake back up.
See discussion here Arduino Yun, power draw - Arduino Yún - Arduino Forum