A Geometric Approach to Fault Detection and Isolation of Continuous-Time Markovian Jump Linear Systems

This paper is concerned with development of novel fault detection and isolation (FDI) strategies for the Markovian jump linear systems (MJLS´s) and the MJLS´s with time-delays (MJLSD´s). First a geometric property that is related to the unobservable subspace of MJLS´s is presented. The notion of a finite unobservable subspace is then introduced for the MJLSD´s. The concept of unobservability subspace is introduced for both the MJLS´s and the MJLSD´s and an algorithm for its construction is described. The necessary and sufficient conditions for solvability of the fundamental problem of residual generation (FPRG) for the MJLS´s are developed by utilizing our introduced unobservability subspace. Furthermore, sufficient solvability conditions of the FPRG for the MJLSD´s are also derived. Finally, sufficient conditions for designing an H_∞-based FDI algorithm for the MJLS´s with an unknown transition matrix that are also subject to input and output disturbances are developed.