A non-conservative approach to set membership identification for control

A polynomial time algorithm for converting time domain input-output data into worst case frequency domain set membership information with arbitrary precision is presented. Experimental data is assumed to be noise corrupted time domain input-output measurements for a single-input single-output linear shift invariant discrete time system. This method uses prior knowledge of bounds on both the output noise and the system impulse response. For a given finite set of frequencies, the identification algorithm calculates the set of all frequency responses which are consistent with the data and bounds. This representation of uncertainty is provably non-conservative in a certain sense for assessment of robust stabilisation of all systems which are consistent with the data and bounds. The results can be used in existing worst case frequency domain identification methods or for non-functional representations of system uncertainty.