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Rejection of Bounded Disturbances via Invariant Ellipsoids Technique

In this paper an approach based on invariant ellipsoids is applied to the problem of persistent disturbance rejection by means of static state-feedback control. Dynamic system is supposed to be linear time-invariant and affected by unknown-but-bounded exogenous disturbances. Synthesis of an optimal controller that returns a minimum of the size of the corresponding invariant ellipsoid is reduced to one-dimensional convex minimization with LMI constraints. The problem is considered in continuous and discrete time cases