Observer-based feedback controller design for robust tracking of discrete-time polytopic uncertain LTI systems

This paper presents an observer–based robust controller for constant reference tracking of linear time invariant systems with polytopic model uncertainties. To this end, this paper not only designs a robust integral controller gain but also suggests how to determine the robust observer gain and the observer model used in the observer. Since the observer model selection is not obvious due to the polytopic uncertainties, particular attention needs to be paid to that. This paper computes the robust controller and observer gains first. Then, the observer model is selected in a way that the whole closedloop is stable and LMIs are used in the middle of choosing the gains and observer model. Simulation examples show that the proposed observer-based feedback control successfully achieves robust reference tracking.