It is shown that for systems which have an input subsystem, with outputs that can be observed, full LQR state-feedback robustness properties can be recovered at the input by only performing the recovery procedure on that section of the Kalman filter representing this subsystem. This has the advantage that the performance of the Kalman filter will not deteriorate as much as when using the full recovery procedure of Doyle and Stein. A procedure is also described for improving the measurement noise rejection properties of the Kalman filter when the recovery procedure is employed. This entails adding a fictitious coloured measurement noise source, allowing the frequency response of the filter to be shaped outside the recovery region. The problem was motivated by marine control problems where input subsystem measurements were accessible.
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