There are Buck/Boost devices (Go to allelectronics.com and check their catalog, then shop other places for a larger seletion)
19.6 times 0.2 is about 3.9 so you should be able to go down to around 15 volts or perhaps a bit less before performance on that TV suffers.. Most House systems are 13.6 That's a bit low.. but I'd try a direct feed. It will not hurt the TV and it **MIGHT** work depending on how much wiggle room they built in.
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Many computer stores have adjustable 12 volt supplies. 19.5 is on the list I thint (you can use 19.anything with that set) So you might try a computer DC power pack from MicroCenter or Frys or some other store. Even Radio Shack has one or google IGO.com