Can a police officer run a speed trap outside their city?

I p through a small town in Illinois on the way to work. Occasionally I will see one of the town's police cars parked in a driveway, presumably monitoring people's speeds. This morning I saw one of the officers parked a half-mile outside of the town, in an unincorporated area. Could this officer cite someone for speeding even if the offense took place outside the town? Based on previous similar questions that have been answered, it sounds like the answer is yes, but I was wondering if Illinois would be different at all.