A Novel Unknown Input Observer Design for Nonlinear LPV Systems

Abstract

This letter presents the design of an unknown input observer (UIO) for linear parameter-varying (LPV) systems, including nonlinearities that are assumed to fulfill one-sided Lipschitz quadratically inner-bounded (OSL-QIB) conditions. The proposed approach introduces a novel extension of conventional LPV frameworks by directly incorporating nonlinear terms, aiming to improve observer performance and reduce the modeling errors typically introduced during the transformation of a nonlinear system into its LPV counterpart. A key contribution of this letter is the development of a UIO design that avoids the state transformation step, which is often highly complex and only valid under restrictive assumptions such as a constant unknown input matrix D. By eliminating this constraint, the proposed observer design significantly enhances scalability and applicability to a broader class of systems. The performance and effectiveness of the approach are demonstrated through both a numerical example and a well-established open-channel flow benchmark: the Corning channel in California, USA.