Mixed H 2 / H ∞ Fault Detection Filter for Markovian Jump Linear Systems

We tackle the mixed H 2 / H ∞ 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 H 2 subject to a given upper value on the H ∞ norm; the second one is the opposite situation; that is, we minimize an upper bound on H ∞ , subject to a given restriction on the H 2 norm; and the third one is the minimization of a weighted combination of the upper bound of both the H 2 and H ∞ 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 H ∞ 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.