Mixed \(H_2 / H_{\infty}\) fault detection filter for Markovian jump linear systems (Q1720897)

Summary: We tackle the mixed \(H_2 / H_{\infty}\) 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 \(H_{\infty}\) norm; the second one is the opposite situation; that is, we minimize an upper bound on \(H_{\infty}\), 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 \(H_{\infty}\) 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 \(H_{\infty}\) 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.