Technical Notes and Correspondence Worst-Case/Deterrninistic Identification in H,: The Continuous-Time Case

In this note, recent results obtained by the authors for worst-case/deterministic H, identification of discrete-time plants are extended to continuous-time plants. The problem considered involves identification of the transfer function of a stable strictly proper continu- ous-time plant from a finite number of noisy point samples of the plant frequency response. The assumed a priori 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 are provided for each algorithm in these plans. These hounds establish that the given plans of algorithms are robustly convergent and (essentially) asymptotically optimal. Addi- tionally, 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 apriori informa- tion and the data cardinality.