Grant Agreement n. 224117Grant Agreement • May 22nd, 2009
Contract Type FiledMay 22nd, 2009Note that the input u is not taken into account in (83). This is not likely to have a major impact on the closed-loop behavior of the process, because usually in the outer mode the state x is relatively far from the origin, and u saturates irrespective to the choice of the stage cost L. Note also that the stage cost (83) is only used in the outer mode: as soon as x(k) enters X0, a constant feedback control loop of the form u(k + j) = Kx(k + j) is applied for all j N0 (see next Theorem 6), where the gain K can be designed with arbitrary (yet stabilizing) performance criteria.