Anti-windup design for rational systems by linear-fractional representation

This study investigates both static and dynamic anti-windup problems for rational systems subject to actuator saturation. New approaches for the synthesis of anti-windup compensators are proposed based on the linear-fractional representation of rational non-linear systems. By using quadratic Lyapunov function and with a modified sector condition, convex optimisation algorithms based on linear-matrix inequalities are devised to maximise the region of attraction and the L₂ bound on disturbances and minimise the L₂-gain from disturbance to performance output. Numerical examples illustrate the effectiveness of the proposed approach.