Robust system identification from weighted impulse response data and worst-case error bounds

The paper describes the problem of identification of a linear discrete-time system in l₁, from noisy impulse response data of the system. Many tuned algorithms using window functions are proposed in the literature for the problem of H_∞ identification. The study concerns the use of suitable window functions and tuned and untuned algorithms for the problem of identification in l₁. The properties of window functions suitable for l₁ identification are analysed and it is shown that the use of a parameterised exponential window function leads to a convergent worst-case error. The optimal value of the window parameter which results in the least worst-case model error is given in terms of the a priori assumptions on the system and the noise. The tuned algorithm using the optimal parameter is proved to be robustly convergent