In this paper, we design a novel PI-like output feedback tracking controller for linear systems subject to state and input constraints. The proposed solution exploits the internal model principle to design via robust positive invariance and the Extended Farkas’ Lemma, a constrained set-point tracking controller. The considered polyhedral setup results in a bilinear optimization design problem that can be solved offline, allowing to simultaneously determine the sets of admissible set-points and plant’s initial conditions. The proposed solution guarantees asymptotic offset-free set-point tracking, local stability, and constraints fulfillment. Simulation results show the effectiveness of the proposed design and contrast it with an alternative scheme.

Geovana Franca dos Santos, Eugenio B. Castelan, Walter Lucia, "On the design of constrained PI-like output feedback tracking controllers via robust positive invariance and bilinear programming", IEEE Control Systems Letters (L-CSS), 2023 (Accepted)