Stability is a critical issue in gain-scheduled control problems in that the closed loop system may not be stable during the transitions between operating conditions despite guarantees that the gain-scheduled controller stabilizes the plant model at fixed values of the scheduling variable. For Linear Parameter Varying (LPV) model representations, a controller interpolation method using Youla parameterization that guarantees stability despite fast transitions in scheduling variables is proposed. By interconnecting an LPV plant model with a Local Controller Network (LCN), the proposed Youla parameterization based controller interpolation method allows the interpolation of controllers of different size and structure, and guarantees stability at fixed points over the entire operating region. Moreover, quadratic stability despite fast scheduling is also guaranteed by construction of a common Lyapunov function, while the characteristics of individual controllers designed a priori at fixed operating condition are recovered at the design points. The efficacy of the proposed approach is verified with both an illustrative simulation case study on variation of a classical MIMO control problem and an experimental implementation on a multi-evaporator vapor compression cycle system. The dynamics of vapor compression systems are highly nonlinear, thus the gain-scheduled control is the potential to achieve the desired stability and performance of the system. The proposed controller interpolation/switching method guarantees the nonlinear stability of the closed loop system during the arbitrarily fast transition and achieves the desired performance to subsequently improve thermal efficiency of the vapor compression system.