Robust fault detection in linear multivariable systems with unknown disturbance is investigated by using Luenberger-type unknown input observers. The main advantage of the given approach is that a residual generator has a lower dynamical order than the system dimension and is thus easier to implement. Moreover in this approach, an observer dually provides more design freedom since it has five coefficient matrices to be designed.
An algorithm for the complete parameterization of all the coefficient matrices of the Luenberger-type unknown input observers are developed. The parameterization is established in terms of some sets of design parameters, the number of which is defined by the order of the residual generator. Finally, a given problem is transformed into the problem of selecting a set of design parameters that satisfy a set of six constraints. The results of a numerical example performed by using the developed algorithm are shown, and it is illustrated that the proposed approach provides all the degrees of design freedom and is simple and effective.