ℒ₂‐Stabilization of continuous‐time linear systems with saturating actuators

Abstract

Abstract This paper addresses the problem of controlling a linear system subject to actuator saturations and to ℒ︁ 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 ℒ︁ 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 © 2006 John Wiley & Sons, Ltd.