The almost disturbance decoupling problem with internal stability for linear systems subject to input saturation-state feedback case

We consider the almost disturbance decoupling problem (ADDP) and/or almost D-bounded disturbance decoupling problem ((ADDP)_D ) with internal stability for linear systems subject to input saturation and input-additive disturbance via linear static state feedback. We show that the almost D-bounded disturbance decoupling problem with local asymptotic stability ((ADDP/LAS)_D) is always solvable via linear static state feedback as long as the system in the absence of input saturation is stabilizable, no matter where the poles of the open loop system are, and the locations of these poles play a role only in the solution of (ADDP/SGA)_D, (ADDP/SGAS)_D or ADDP/GAS where semi-global or global asymptotic stability is required