Nonlinear control of double integrator plant with saturation

The control of plants with inputs limited by saturation is a difficult problem, but of great practical importance. This paper considers a double integrator plant with input saturation. A new controller is designed, based on Zubov's theorem from nonlinear stability theory. The controller is nonlinear. The most significant feature of this controller is that it enables the designer to choose the domain of attraction of the closed loop system. Simulation results are presented to confirm the controller performance.