Your 2 batteries probably have a capacity of about 200 Ampere Hours (AH). For good battery life you should only use half of the capacity, so if the batteries are fully charged, you have about 100 AH available.
Your 1100 Watt inverter is capable of drawing 100 Amps at 12v. One hour of this will be 100 AH.
To give you any help we need to know what you are using the inverter for, as 2oldman asked.
If you have a voltmeter let us know what the battery voltage is when the sun goes down and the inverter is drawing current.