Region of attraction estimates for LPV-gain scheduled control systems

Recent methods for gain scheduling controller design based on linear parameter-varying (LPV) systems offer a systematic way to obtain a nonlinear controller that covers different operating conditions. However, despite that the LPV synthesis part of the process of obtaining a gain scheduled controller is theoretically straight forward, the nonlinear closed loop system may be unstable for some operating conditions. This property is illustrated by a simple second order autonomous nonlinear system, the well known Van der Pol equation. Furthermore, a region of attraction estimate based on the LPV analysis for the nonlinear system is given.