I can and I have a glass top stove. Now I admit that I have canned on my stove but I was very uncomfortable the whole time. After putting a lot of thought into the problem and thinking it was best to consider the warnings, I found a solution. And in fact, my solution makes canning easier in my small kitchen.
I purchased the Cadco PCR-1S Professional Cast Iron Range, $134. at Amazon.
I have an All American Pressure canner and when filled with food, jars and water plus the weight of the canner it becomes all I can lift. In choosing a hot plate I knew I need one the could handle the weight and I only needed one burner. The Cadco was the perfect answer. I have very little space to can and using the hot plate has made canning much easier. I have a cart with wheels. The cart is sturdy enough to hold the weight of my canner. I put the cart near my stove and it is easy to move the filled jars from the stove to the canner. The whole thing works extremely well. My Cadco is very sturdy and has held up to over 4 years of canning. If you have a similar problem you may be able to fine a less expensive hot plate but it must be sturdy and make sure it will work with aluminum.
I hope this gives you some ideas. Enjoy the fruits of your labor. Any questions please ask.