A Nonlinear Controller for Input Amplitude and Rate Constrained Linear Systems

This technical note presents a nonlinear state feedback controller for systems with linear dynamics subject to an amplitude and rate limited actuator. The nonlinear state feedback facilitates faster convergence compared to linear state feedback while guaranteeing domains of attraction of similar size. The parametrization of the controller is done solving a convex optimization problem based on linear matrix inequalities (LMIs). Finally, an example illustrates that the controller achieves large stability regions and short settling times.