Discrete-time LPV Systems with Inexact Scheduling Parameters: an Unknown Input Observer Design approach

Abstract

In this paper, a novel unknown input observer (UIO) design for discrete-time linear parameter-varying (LPV) with inexact scheduling parameters is addressed. The proposed approach is particularly relevant as most LPV design conditions require that the time-varying parameters of the system are completely known and real-time available. Therefore, such strategies do not present adequate formulations to deal with such types of uncertainty. Moreover, UIOs have significant applications in different areas, such as fault detection and isolation problems. Existence conditions for the UIO are provided in order to properly handle the mismatch along with the presence of unknown inputs in the LPV system. The design conditions are based on an input-to-state stability approach obtained from a parameter-dependent Lyapunov function and are cast in the form of Linear Matrix Inequalities. The effectiveness of the proposed methods is illustrated using a numerical example.