The design of a controller for a nonlinear system that provides, at the same time, the desired performance, a tractable implementation and an easy performance analysis is still challenging. A popular approach to tackle this issue is to linearize the system at relevant operating points and then take advantage of some wellknown linear design tools. The system can then be modeled as a linear parameter varying (LPV) system. When a single controller is not able to perform as required, gain scheduling methods may be used: multiple controllers are designed throughout the operating range and then interpolated. Popular in aeronautics due to the early failures of adaptive control, the key of its stability was only understood in the late eighties. 1 Even though the principle of gain-scheduling is straightforward, it still raises many practical problems. 2 In particular, as each controller is designed independently, there is no guarantee that the final interpolated