I have a Sony Bravia TV KDL-55W805B which unfortunately has Sony's own Smart TV software installed, and not Android TV which newer Sony TV's have. Is there any way for me to install Android TV on my TV and replace the Sony Smart TV? I hate that I am stuck with a discontinued TV software that doesn't get any updates or new apps.
NO. NO. NO. NO. The hardware is different and so is the kernel. Its just not supported Unless one of The devs around ports it to the tv which is highly unlikely
You could use a compatible Android TV Stick, to access similar features of other newer Sony TVs with in-built Android TV software. Most of these are available on eBay.
You can still stream through various genres:
YouTube
XBMC
Netflix
Showbox etc
You connect your Android TV stick to the HDMI input of the LED TV and make it a Smart TV
NB Check compatibility first