L2performance design problem for systems presenting nested saturations

This paper addresses the problem of stabilization for systems presenting nested saturations and L2limited disturbance. The L2performance design problem of the system are studied. LMI conditions and associated convex optimization problems are proposed in order to determine both an inner and an outer ellipsoids. Indeed, the closed-loop trajectories remain bounded in the outer ellipsoid despite the action of the disturbance provided that the initial states are starting from the inner ellipsoid. In addition, it is also derived a condition which allows to synthesize the saturating gains in order to minimize the L2gain from the disturbance to the controlled output by the solution of an LMI optimization problem.