Generalized set-theoretic unknown input observer for LPV systems with application to state estimation and robust fault detection

This paper proposes to design an unknown input observer (UIO) for the linear-parameter-varying (LPV) system on the basis of the set theory, which is named as the set-theoretic UIO (SUIO). The advantage of the SUIO consists in that it combines active and passive approaches to obtain robustness in state estimation (SE) and fault detection (FD). The active approach is based on the use of UIO to decouple unknown inputs, while the passive approach is based on the set theory to bound uncertain factors that cannot be actively decoupled. As a result, the effect of both unknown inputs (process disturbances, modeling errors, etc.) and measurement noises can be appropriately handled in the residual signals compared with the standard UIO-based SE and FD approaches. The design of SUIO can overcome the limitations of the traditional UIO design conditions, which can significantly broaden the application of the UIO-based SE and FD theory. Moreover, this paper proposes a generalized framework that can provide more flexibility in the design of SUIO guaranteeing their stability by means of a group of matrix inequalities. Because the LPV system uses a collection of online obtainable scheduling variables to embed nonlinearities, the design of SUIO for the LPV system can be used to address the SE and FD problems of nonlinear systems. At the end of this paper, two case studies are used to illustrate the effectiveness of the proposed approach.This work was supported by the Natural Science Foundation of Guangdong (no. 2015A030313881), the National Natural Science Foundation of China (no. 61673239), the Shenzhen Key Lab of Space Robotic Technology and Telescience, the Spanish Government (MINECO) through the project CICYT ECOCIS (ref. DPI2013-48243-C2-1-R), and MINECO and FEDER through the project CICYT HARCRICS (ref. DPI2014-58104-R).Peer Reviewe