Global Regulation of Input-Saturated Discrete-Time Linear Systems Subject to Persistent Disturbances

Abstract

A novel control strategy for globally stabilizing inputsaturated linear plants subject to persistent, arbitrarily large but bounded, disturbances is described. The technique is based on a weaker concept of robust positive invariance, referred to in the paper as positive quasi d-invariance, which is believed to be new and allow the achievement of better control performance if compared with those resulting from using actual control strategies based on the classical notion of positive d-invariance. Simultaneous global internal asymptotic stability and semiglobal external finite-gain BIBO stability is achieved under critical structural conditions on the disturbance-to-state map of the plant. Finally, an example is presented where the achievable regulation performance is shown and contrasted with those achievable by a control solution based on the classical notion of positive d-invariance.