On Lp (lp) performance with global internal stability for linear systems with actuators subject to amplitude and rate saturations

It has been shown that for critically unstable 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 is an element of [1, infinity). In this paper we show that for null controllable systems with actuators subject to amplitude and rate saturations, the L-p (l(p)) performance (without finite-gain) with global internal stability can be achieved.