The hard wired Ethernet device which is presented as eth0 in Android is configured for DHCP by default. I do not see any settings options in Network Settings that allow me to change the configuration for eth0 to a static IP address.
If I use ifconfig on the android shell I can get it a static ip address configured but it's not persistent across reboots. Additionally, if the network that the device is plugged into has a DHCP server, the DHCP client on Android will take over the IP address in short order.
I tried adding in my ifconfig commands in /persist/eth0.sh but they do not work. I confirmed my script is written correctly by running it after boot. I think that after the eth0.sh script runs the network manager wipes the settings during the boot process.