Anti-windup strategy for reset control systems

This paper proposes an anti-windup strategy to deal with stability and performance requirements for a class of hybrid systems, such as those including a reset controller and subject to input saturation. The computation of the anti-windup compensator aiming at ensuring both L2 input-to-state stability and internal stability of the closed-loop system is carried out from the solution of matrix inequalities. Depending on the way chosen to describe reset rules, the conditions for designing the anti-windup compensator are expressed through nonlinear matrix inequalities or linear matrix inequalities. Some optimization criteria in both cases are considered for the synthesis purpose: maximization of the L2-norm upper bound on the admissible disturbances for which the trajectories are assured to be bounded; minimization of the L2-gain of the disturbance to the system to-be-controlled output; and the maximization of an estimate of the domain of attraction of the origin.