There are robotic and industrial control applications where the control action must be updated faster than the output measurement. This fact leads to multirate controllers. In this paper, it is exposed an algebraic design which is used to design minimum and finite time controllers based on the resolution of a coupled diophantine equations for different sampling rates. Also, it is explained the way in which these equations are solved. Finally, a cancellation controller is designed to control an interesting robotic environment case. Promising results are obtained.