Grass killers are selective; they only kill turf grass and weeds in turf grass. What you have is an ornamental, perennial grass that might be on the list of invasive plants in Michigan (http://forestry.msu.edu/Mipc/tool.htm). Try killing it with Glyphosate, the active ingredient in Round-Up, which kills any plant. You might also want to get in touch with your county extension service or master gardeners program. They can come out and identify the grass, and might have standardized procedures for dealing with it so that it doesn't come back.