Control design for linear systems with saturating actuators and ℒ2-bounded disturbances

This paper addresses the problem of synthesis of state feedback control laws for systems subject to L₂-bounded disturbances in presence of saturating actuators. Conditions that allow to guarantee both the internal and external stability of the closed-loop system are proposed. They are formulated from the use of the Finsler´s lemma and a generalized sector non-linearity description. This approach allows to introduce new variables (multipliers) in the problem which increase the degrees of freedom in the synthesis problem. Based on the stability conditions, a multiobjective problem is addressed: the synthesis of a state feedback gain that simultaneously maximizes the magnitude of the admissible L₂-disturbance and the size of the domain of stability of the closed-loop system.