When we moved 3 years ago, I gave up my wonderful gas JennAir (stayed with the house when we sold) and 'inherited' a glass top. I don't know if all glass tops cycle on/off when heating, but this one did. I never did find that sweet spot where a soup or stew would continue to gently simmer, and my canning that first year was a nightmare. I was told later, that you are not supposed to use a canner on a glass top.
When we remodeled the kitchen the next year, I was absolutely thrill to see the backside of that glass top range, and return to gas. I don't even mind the extra cleaning!