Tracking controller for intrinsic output saturated systems in presence of amplitude and rate input saturations

We consider the problem of controlling plants that are subject to multiple saturation constraints. Especially, we are interested in linear systems whose input is subject to amplitude and rate constraints of saturation type. Furthermore, the considered systems output is also subject to an intrinsic saturation. Then, aiming to design global (and asymptotic) output tracking of compatible output-reference trajectories, we propose a suitable saturated linear controller following the direct approach (where the constraints are taken into account during the regulator design). The (non-linear) closed-loop control system is analyzed using input-output stability tools. Thus, conditions guaranteeing l₂-tracking performances are formally defined. Interestingly, the proposed controller is shown to ensure perfect output-reference tracking in presence of varying with l₂-vanishing rate inputs. On the other hand, in the case of arbitrary inputs, the proposed controller guarantees that the less changing the inputs are the better the output-reference tracking.