H∞-almost disturbance decoupling with internal stability for linear systems subject to input saturation

For a linear system subject to input saturation and input-additive disturbances, we show that: 1) the H_∞-almost disturbance decoupling problem with local asymptotic stability is always solvable via state feedback as long as the system. In the absence of saturation is stabilizable, no matter where the open loop poles are; 2) the H_∞-almost disturbance decoupling problem with semi-global asymptotic stability is solvable via state feedback as long as the system in the absence of saturation is stabilizable with all its open loop poles located in the closed left-halfplane; and 3) the H_∞-almost D-bounded disturbance decoupling problem with global asymptotic stability is solvable via state feedback as long as the system in the absence of saturation is stabilizable with all its open loop poles located in the closed left-half plane. The first two results generalize those in Lin et al. (1996) by not requiring the disturbance to be bounded by a known bound, or even bounded. The third result generalizes those in Lin et al. in two ways: the open loop system does not have to be asymptotically stable, or even critically stable; and the disturbances can be either magnitude bounded or energy bounded