Möbius transform and efficient LPV synthesis

As an extension of the robust H_∞ method, the time domain design based on linear matrix inequalities (LMI) presented in [10] is an appealing and conceptually simple framework to obtain robust LPV controllers, however, the resulting controller is not always suitable for implementation. This paper shows that in a variant of the S-procedure how the multiplier is transformed if the parameter domains are related through a Möbius transform. Based on this result, if certain conditions are fulfilled, the paper provides a numerical reliable method to compute and parametrize all the scheduling variables of the LPV controllers that correspond to a given multiplier matrix and can be expressed in terms of the scheduling variables of the plant.