Identification in \({\mathcal H}_ \infty\) using Pick's interpolation (Q2367116)

Robust identification in \(H_ \infty\) of SISO system from the uniform noisy frequency response samples is considered. The interpolation approach, based on the Pick interpolation theorem, is applied to derive the system model, where the standard polynomial interpolation is replaced by the use of more parsimonious rational interpolation. First, the noise free case is considered and the existence of interpolation function convergent to the true model is shown. Next, the problem for noisy measurement data is considered and the tuned interpolation algorithm, with modification of the data, is introduced. The worst-case identification error bound is given. The particular feature of the approach is that the identified model lies in the same class as the true, unknown system. An illustrative example is included.