Mixed Fault Detection Filter for Markovian Jump Linear Systems

We tackle the mixed fault detection filter problem for a Markov jump linear system (MJLS) in the discrete-time domain. We present three distinct formulations: the first one is to minimize an upper bound on the subject to a given upper value on the norm; the second one is the opposite situation; that is, we minimize an upper bound on , subject to a given restriction on the norm; and the third one is the minimization of a weighted combination of the upper bound of both the and norms. We present new conditions in the form of linear matrices inequalities (LMI) that provide the design of the fault detection filter. We also present results for the so-called mode-independent case and the design of robust filters in the sense that the system matrices are uncertain. In order to illustrate the feasibility of the proposed approaches, a numerical example is presented.