Asynchronous Fault Detection H2 Filter For Markov Jump Linear Systems

Leonardo de Paula Carvalho; André Marcorin de Oliveira; Oswaldo Luiz do Valle

doi:10.48011/asba.v2i1.1021

Leonardo de Paula Carvalho Universidade de São Paulo
André Marcorin de Oliveira Universidade Federal de São Paulo
Oswaldo Luiz do Valle Universidade de São Paulo

DOI: https://doi.org/10.48011/asba.v2i1.1021

Keywords: Fault Detection, Markovian Jump Linear System, H2 norm

Abstract

This work focuses on the Fault Detection (FD) problem in the Markovian Jump Linear System framework for the discrete-time domain, under the assumption that the Markov chain mode is not directly accessible. This assumption poses new challenges, since the filter responsible for the residue generation no longer depends on the Markov chain mode. For modeling this type of situation, a Hidden Markov chain (O(k), Ô(k)) is considered, with O(k) corresponding to the hidden part and Ô(k), to the observable part. The main result is the design of an H2 Fault Detection Filter (FDF) that depends only on the estimated mode Ô(k), obtained through a formulation based on Linear Matrix Inequalities (LMIs). In order to illustrate the usability of the proposed approach, we consider as an illustrative example a plant with coupled tanks subject to two distinct faults.