Multistage gamma-level control for input-saturated systems with disturbances

Abstract

For input-saturated systems with disturbances, states in the domain of attraction cannot converge to the origin, but only to neighborhood around it. In order to design the smallest possible target invariant set and the largest possible domain of attraction, in this paper, we introduce a multistage gamma-level control for achieving a smaller target invariant set within a given performance level and a larger domain of attraction than results obtained in previous studies. In particular, for the case in which the disturbances satisfy a matched condition, this paper introduces an control with an extra control part to perfectly reject these disturbances despite the uncertainties; the introduction of the control with an extra control part causes the target invariant set to shrink to the origin and the performance level to become zero.