On worst-case approximation of feasible system sets via orthonormal basis functions

This paper deals with the approximation of sets of linear time-invariant systems via orthonormal basis functions. This problem is relevant to conditional set membership identification, where a set of feasible systems is available from observed data, and a reduced-complexity model must be estimated, within a linearly parameterized model class. The basis of the model class is a collection of impulse responses of linear filters (e.g. Laguerre functions), whose poles must be chosen properly. The objective of the paper is to select the basis function pole according to a worst-case optimality criterion taking into account the uncertainty system set. This leads to complicated min-max optimization problems. Suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors