L2-stabilization of continuous-time linear systems with saturating actuators

This paper addresses the problem of controlling a linear system subject to actuator saturations and to L-2-bounded disturbances. Linear matrix inequality (LMI) conditions are proposed to design a state feedback gain in order to satisfy the closed-loop input-to-state stability (ISS) and the closed-loop finite gain L-2 stability. By considering a quadratic candidate Lyapunov function, two particular tools are used to derive the LMI conditions: a modified sector condition, which encompasses the classical sector-nonlinearity condition considered in some previous works, and Finsler's Lemma, which allows to derive stabilization conditions which are adapted to treat multiple objective control optimization problems in a potentially less conservative framework. Copyright (C) 2006 John Wiley & Sons, Ltd.