Robust Fault Detection H∞ Filter for Markovian Jump Linear Systems

This paper studies the robust fault detection problem associated with Markovian Jump Linear Systems (MJLS) in the discrete-time domain. The approach presented consists in using a MJLS filter as a residual generator designed via Linear Matrix Inequalities (LMI) and formulated as an $H_{\infty}$ filter problem. We tackle three situations: designing an $H_{\infty}$ filter that depends on the Markov mode; the so-called mode-independent case; and the design of robust $H_{\infty}$ filters in the sense that the system matrices are uncertain. A numerical example is presented in order to illustrate the feasibility of the proposed solution.