Optimal finite-sample experiment design in worst case l 1 system identification

Finite-sample optimality properties are investigated for the worst case l₁ identification of the impulse response of discrete-time linear time-invariant systems. The experimental conditions considered consist of one or more finite input-output sequences. The measured outputs are corrupted by additive disturbances, known only to be componentwise-bounded. Optimality of the experimental data is measured by the diameter of information. It is shown that, if the system has finite memory n+1 and at most n+1 output values are measured, then the number of experiments that define optimal information must be exponential in n. It is also shown that, in the case of one input and no a priori information, the impulsive input is optimal