Matrix of Inception in Real world

It's almost certainly possible, how soon it will happen is a much bigger question. Now, the Inception model for controlled dreams has very little basis in science, but the Matrix model is very realistic. All of our perceptions and our control of our own physical bodies are based on electrical impulses in our nervous systems. If we can read and duplicate those accurately enough, there's no reason we couldn't interface our brains directly with a computer. 
 
The challenges are figuring out how to read information from our nerves, write information to our brains, and create a computer simulation convincing enough to fool us. The first two are under active study (though still in very rudimentary stages). The last is probably just a matter of time. Think of how far video games have come in the last twenty years. In the next decade or two, I suspect video game environments will be complex enough that our eyes can't distinguish them from reality. Fooling the other senses will follow in good time.
 
Now, how long this will take is a matter of guesswork. I don't really expect convincing virtual reality to happen in my lifetime. But then I didn't think I'd see a combination cell phone/camera/scanner/wireless modem/palmtop computer before I was twenty , and it happened before I turned twenty-five. If technology continues to advance, I think it's inevitable in the long run.