A globally stabilising controller under saturated input for linear planar systems with one unstable pole

Controllers for planar systems with one stable and one unstable pole under saturated input are considered. The requirements are: (i) global stability, i.e. the region of attraction is the null controllable region, (ii) possibility of enforcing any desired performance around the origin, and (iii) no chattering of the control signal in the presence of noise. A simple continuous nonlinear state feedback controller is proposed that satisfies all these requirements. The performance of the proposed controller is compared in simulation with that of classical controllers such as linear state feedback and time optimal controllers.