Abstract
This paper addresses the problem of controlling a continuous-time linear system subject to actuator saturations and to L2-bounded disturbances. We propose LMI conditions that allow to design a state feedback saturating control law in order to satisfy the closed-loop Input-to-State stability (ISS). 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 previous works, and Finsler’s Lemma, which allows to derive stabilization conditions which are potentially adapted to be cast into multiple objective control optimization problems. Relative to a previous work which proposed BMI conditions for treating a similar problem, the given LMI conditions allow to propose a more efficient convex programming design technique.
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