L₂control of LPV systems with saturating actuators: Põlya approach

This paper addresses the design problem of L₂, gain-scheduling non-linear state-feedback controller for linear parameter varying (LPV) systems, subjected to actuator saturations and bounded energy disturbances, by using parameter-dependent type Lyapunov functions. The paper provides a systematic procedure to generate a sequence of linear matrix inequality (LMI) type conditions of increasing precision for obtaining a suboptimal L₂ state-feedback controller. The presented method utilizes the modified sector condition for formalization of actuator saturation and homogeneous polynomial parameter-dependent representation of LPV systems. Both simulations and experimental studies on an inverted pendulum on a cart system illustrate the benefits of the approach.