Stray cats coming through doggy door

Question
I have a doggy door for my two small dogs.  As of late the neighborhood is being overrun with cats.  While I do not dislike cats, I am a dog-person; further, I have family who is allergic to cats - essentially I cannot have cats in my home.  These cats are finding their way in through the doggy door which I need for my dogs who are trained for such.  
How do I keep these cats out of my home (without doing something unspeakable)?

Answer
Hi Stacy,

I have the opposite problem. I need to keep cats in the house and let the dogs in and out. I use this; http://www.petdoors.com/electronic_pet_doors.htm
There are different types. But a locking type door will take care of your problem. Good luck.

Ciao, Karen