Worst-case/deterministic identification in H∞ : the continuous-time case

Results obtained by the authors (1991) worst-case/deterministic H_∞ identification of discrete-time plants are extended to continuous-time plants. The problem involves identification of the transfer function of a stable strictly proper continuous-time plant from a finite number of noisy point samples of the plant frequency response. The assumed information consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, an upper bound on the roll-off rate of the plant, and an upper bound on the noise level. Concrete plans of identification algorithms are provided for this problem. Explicit worst-case/deterministic error bounds for each algorithm establish that they are robustly convergent and (essentially) asymptotically optimal. Additionally, these bounds provide an a priori computable H_∞ uncertainty specification, corresponding to the resulting identified plant transfer function, as an explicit function of the plant and noise prior information and the data cardinality