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

This note 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. The basis of the model class is made of impulse responses of linear filters. The objective of the note is to select the basis function poles according to a worst-case optimality criterion. Suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors.