Linear Parameter-Varying Control of Nonlinear Systems based on Incremental Stability

The Linear Parameter-Varying (LPV) framework has long been used to guarantee performance and stability requirements of nonlinear (NL) systems mainly through the L2-gain concept. However, recent research has pointed out that current L2-gain based LPV synthesis methods can fail to guarantee these requirements if stabilization of a non-zero operating condition (e.g. reference tracking, constant disturbance rejection, etc.) is required. In this paper, an LPV based synthesis method is proposed which is able to guarantee incremental performance and stability of an NL system even with reference and disturbance rejection objectives. The developed approach and the current L2 LPV synthesis method are compared in a simulation study of the position control problem of a Duffing oscillator, showing performance improvements of the proposed method compared to the current L2-based approach for tracking and disturbance rejection.