LMI-based Robust PI Unknown Input Observer Design for Discrete-time LPV Systems

In this paper, a novel unknown input observer (UIO) design procedure for discrete-time linear parameter-varying (LPV) systems is presented. Differently from other UIOs approaches in the literature, this one focused in using a robust proportional-integral UIO (PI-UIO) with an explicit integrator variable to estimate the states and unknown inputs. First, a discussion concerning the convergence condition for the existence of the PI-UIO is provided. Second, a set of Linear Matrix Inequalities (LMIs) based conditions for H-infinity performance was derived to obtain the observer gain synthesis and minimize the effect of exogenous disturbances in the signals estimations. The effectiveness of the proposed formulation is evaluated through a numerical example, where a proportional UIO and the proposed PI-UIO performances are compared.