Algorithms for robust identification in \({\mathcal H}_\infty\) with nonuniformly spaced frequency response data (Q1265427)

The problem of linear system identification in \(H_\infty\) is considered. First, a least-squares-based two-stage identification algorithm of the frequency response function from non-uniformly spaced noise-corrupted samples is proposed. For the amplitude bounded measurement noise the worstcase error of the algorithm is investigated for exponentially stable discrete-time systems. It is shown that the algorithm is robustly convergent and that in the noise-free case its convergence rate is faster than polynomial rates. Next, a minimax algorithm that achieves the best possible rate of convergence for noise-free measurements is introduced and investigated. Sensitivity of the algorithms to small variations in the frequency sample values is studied and the corresponding conditions for robust convergence of the algorithms are established. To illustrate properties of the algorithms, a simulation example is included.