Any public library, including privately incorporated public libraries, the Dover Public Library established pursuant to 60 Del. Laws, c. 158 and public library systems established pursuant to Chapter 8 of Title 9 may be eligible for state assistance in library construction costs, with the state share representing up to 50% of the total cost of such library construction project. State funding of library construction may be requested in phases and could be authorized over more than 1 fiscal year.