This paper addresses the design of robust multiple model adaptive controllers (RMMAC) for linear parameter varying (LPV) systems using bilinear matrix inequalities (BMI). We show a novel method that allows increasing the performance of the RMMAC when the uncertain parameters of the system dynamics are time-varying (TV). We assume that these TV parameters cannot be measured on-line and that the only information available is on the corresponding slope of variation bound and on the admissible range. A comparison between mixed-μ and BMI/LPV controllers is presented and the benefits of this new approach are assessed using a set of Monte-Carlo simulation runs. The decrease of the RMS of the error due to the use of the BMI/LPV controllers serves as an indicator of the performance improvements of this methodology. An increase of 20% in terms of RMS performance is obtained for the case study presented.