Scheduled controllers for linear systems with bounded actuators: Slab condition

For linear systems under bounded actuators, a new scheduling scheme is used to improve the performance of the closed-loop system, in disturbance attenuation problems. The approach selects the controller, among a continuous family of controllers, that provides the best performance while avoiding saturation, based on the closed-loop behavior (i.e., the closed-loop state vector). As a result, the controller has a quasi linear parameter varying structure. Graphically, the resulting scheduling scheme relies on slab regions of the phase plain. Numerically, the family of the controllers are based on linear splines, and can be obtained by standard LMI software. Benefits of the proposed scheduling scheme is demonstrated through a numerical example.