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

• Published in: International journal of robust and nonlinear control Vol. 16; no. 18; pp. 935 - 944
• Main Authors: Castelan, E B, Tarbouriech, S, da Silva Jr, J M Gomes, Queinnec, I
• Format: Journal Article
• Language: English
• Published: 01-12-2006
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.1118

This paper addresses the problem of controlling a linear system subject to actuator saturations and to 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 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.