Its very simple to set to fix static IP address in your Intel Edison board, You need edit  a file  /etc/wpa_supplicant/wpa_cli-actions.sh 

Move your cursor to around the line 50,

$ vi /etc/wpa_supplicant/wpa_cli-actions.sh

if [ "$CMD" = "CONNECTED" ]; then
    kill_daemon udhcpc /var/run/udhcpc-$IFNAME.pid
    udhcpc -i $IFNAME -p /var/run/udhcpc-$IFNAME.pid -S
fi


The above configuration based on dhcp (Dynamic Host Configuration Protocol ) so, command that line and add your static IP address.

Updated lines:


if [ "$CMD" = "CONNECTED" ]; then
    kill_daemon udhcpc /var/run/udhcpc-$IFNAME.pid
#   udhcpc -i $IFNAME -p /var/run/udhcpc-$IFNAME.pid -S
    ifconfig $IFNAME 192.168.1.100 netmask 255.255.255.0
    route add default gw 192.168.1.1
fi


Note :  If the above configuration did not changed to static IP address, check in your image whether installed latest version in your board.