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Robust Kalman Filtering of Descriptor Systems Subject to Linear Fractional Uncertainties

A robust Kalman type recursive filter has been proposed for descriptor systems subject to unstructured additive uncertainties, which is generalized to linear fractional structured uncertainties in this paper. It is proved that the linear fractional uncertainties during filtering can be represented by the intersection of a series of additive uncertainties relying on the actual plant. A set of additive uncertainties independent of the actual states is utilized in this paper to include this intersection, whose parameters can be obtained offline through convex optimizations. Numerical simulations show that for linear fractional uncertainties, the algorithm can be realized recursively. Moreover, for structured additive uncertainties, the algorithm performs better than the available one.