Without knowing what your actually running how can I suggest a possible power source???
Simply check all your items for onboard fusing, as an example;
head unit = 10amps
mono amp = 100amps
4ch amp = 60amps
Total max draw 170amps
playing 0dB test tones at full tilt = 170amps, (55ah batt = not long lol).
playing music at full tilt = approx 85amps, (55ah batt = 40mins ish).
playing music at half head unit volume = 20amps approx, (55ah batt = 2hrs or so).
I've ran a home setup for a few months using a battery & permanently connected battery charger, I know of a few other people who have also done it....
If running a small system you may get away with a large 12v reg comp power supply, but I wouldn't recommend it.....
Anyhow, all this means nothing until you actually confirm what you need to power.....
CHECK THIS OUT