You can use ping. Although ping failure doesn't necessarily mean that your system is down, it can also happen if the network is down but I believe for most intents and purposes these are same thing. You can use following script

#!/bin/bash

HOSTS="cyberciti.biz theos.in router"



COUNT=4



for myHost in $HOSTS

do

  count=$(ping -c $COUNT $myHost | grep 'received' | awk -F',' '{ print $2 }' | awk '{ print $1 }')

  if [ $count -eq 0 ]; then

    # 100% failed 

    echo "Host : $myHost is down (ping failed) at $(date)"

  fi

done  

This is from here. You can also setup a cron job for this or any similar script to ping all your servers after a regular interval.