Simultaneous L_p-stabilization and internal stabilization of linear systems subject to input saturation - state feedback case

We consider the problem of simultaneous finite gain L_p-stabilization and internal stabilization of linear systems subject to input saturation via linear static state feedback. We show that bounded input finite-gain L_p-stabilization and local asymptotic stabilization can always be achieved simultaneously no matter where the poles of the open loop system are, and the locations of these poles play a role only when bounded input finite gain L_p-stabilization and global or semi-global stabilization are required simultaneously