Comments on "Robust Kalman Filter for Descriptor Systems

In the comments provided in [1], the authors showed that through off-line convex optimization, the filter performance of [2] can be improved through an appropriate combination of ellipsoids determined by the actual plant states and structured model uncertainties. These guidelines are interesting and useful to improve the performance of the filter we proposed in [2]. However, based on simulation results, the authors claimed that they have found a contradiction in Remark 4.1 of [2]. They claimed that when the robust descriptor filter of [2] collapses to a robust filter for standard state-space systems, this filter may perform worse than that proposed in [3]. In order to understand our reply, let us first remember that the uncertain system we are considering is given by