We study a version of the problem. An inverted pendulum-a stick with amass-sits on a cart. The pendulum is hinged to the cart and is free to pivot.The cart is

controlled by a horizontal force exerting on the cart. It is the input for balancing the stick. The modeling of the system follows. We may all have the experience of balancing a stick on our fingertip or on our hand. It is an exercise most of us can learn to do. Watching the leaning of the standing stick and moving our hand we can keep it upright. Balancing a stick is clearly a dynamic act and it requires feedback.