On achieving Lp (lp) performance with global internal stability for linear plants with saturating actuators

We show that for both continuous-time and discrete-time critically unstable linear systems with saturating actuators one can not simultaneously achieve the global internal stabilization and the global finite-gain L_p (l_p) performance whenever the external input (disturbance) is not input-additive. However, one can achieve the global internal stabilization and global L_p (l _p) stabilization (without finite-gain) for any p∈[1:∞)