Mixed H2/H∞ Fault Detection Filter for Markovian Jump Linear Systems

We tackle the mixed H2/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 H2 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 H2 norm; and the third one is the minimization of a weighted combination of the upper bound of both the H2 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.