Following method does not require a static address or messing with the router and any firewalls you may have. See if it will work for your purposes.
Assume you have a PC connected to the Internet that can talk to the home security system. Put TeamViewer
on the PC at home. Set it up by following
but instead of selecting the Basic Installation use the second option Installation to access this PC remotely (Unattended)
It will have you set a password for remote access. Use a good one and make sure you remember it. Also write down the number it gives you have Your ID:
Make sure the PC does not shutdown/hibernate/sleep. (Control Panel, Power Options, High Performance) It's OK for the display to shutdown.
Now put TeamViewer on another PC.
I think this will also work on Android or iPhone (should be able to get it through the usual App store routine) but I have never tried it. You can also download TeamViewer Portable (from the main download page) and put it on a USB drive so you can plug it into any PC.
Run TeamViewer on your remote PC or whatever and put in the number (Your ID:) that you saved in the initial installation and the password. It will show your the desktop of the PC you are trying to reach and then you can do the same things you would do if standing in front of it.