Comments on "Robust Kalman Filter for Descriptor Systems

In the above paper, a Kalman-type robust filter is derived for descriptor systems on the basis of the framework suggested in . The performance of the resulting descriptor filter in , however, is generally not very good, as structured perturbations in the corresponding regularized least-squares problem are directly replaced by unstructured ones. In this comment, we show that through off-line convex optimization, the filter´s performance can be improved without sacrificing its recursiveness. The idea is to use the ellipsoid with the smallest volume to replace the intersection of several ellipsoids that are determined by the actual plant states and structured model uncertainties, and to re-scale the inputs and outputs of a model uncertainty block with the semi-axes of the optimal ellipsoid. Using the same numerical example and design parameter, the variance of the estimation error can be reduced by approximately 10%. Moreover, it has been shown by simulations that when a standard state-space model is adopted and model uncertainties do not include zero, the method of does not always outperform that of .