The objective of this work is to solve the problem of fast dynamics which appears in the synthesis of LPV controllers using a single quadratic Lyapunov function. This can be a serious problem for controller implementation or computer simulation. The solution is achieved by means of an extra LMI added to the set of LMI's used to design the controller. This LMI defines the region where the poles of the "frozen" LTI closed loop system will be.