A thorough methodology to design robust adaptive controllers for uncertain Linear Parameter Varying (LPV) systems, with stability and performance guarantees, is presented. Multiple-Model Adaptive Control (MMAC) strategies are adopted, due to their advantages in terms of design and implementation. Hence, the core of this thesis is devoted, on the one hand, to the design of high-performance Local Non- Adaptive Robust Controllers (LNARCs) and, on the other, to the development of enhanced decision subsystems. The design of LNARCs, robust against parametric and complex-valued uncer- tainties, and which are able to cope with time-variations of the dynamics of the plant, is tackled resorting to an optimization procedure with Bilinear Matrix Inequalities (BMIs) constraints. A novel supervisor for MMAC architectures – the Stability Overlay (SO) – is also proposed, enabling closed-loop stability guarantees for uncertain and time-varying environments. A whole new approach to MMAC is also introduced, that relies on Set-Valued Ob- servers (SVOs) to falsify regions of uncertainty. This control architecture, referred to as MMAC/SVO, guarantees, under mild assumptions, stability and performance for the closed-loop system. Moreover, the developed model falsification strategy is also applied to Fault Detection and Isolation (FDI). As a caveat, the computational requirements of the SVOs can be higher than the alternatives.