Ellipsoidal approximations to attraction domains of linear systems with bounded control

We are concerned with characterization of attraction domains for linear state-space systems. Considered are bounded linear state feedback control and saturated control. Attraction domains for such systems are described in terms of invariant ellipsoids using LMI-based techniques and semidefinite programming (SDP). For systems with saturated control, the ideology of absolute stability is adopted. An application to nonlinear systems is provided.