Identification under Frequency Domain Bounded Dynamical Perturbations

A parameter identification task, motivated by the study of robust adaptive control, is examined. The received signal is assumed to be corrupted not by stochastic noise, but by the presence of a linear dynamical operator which is unknown except for certain frequency domain bounds. The corruption may enter in an additive form, a multiplicative form, or both. The simplest case is found to be the case of additive perturbations to the identification signals, which arise from stable factor perturbations of the system dynamics. A general parametric identification scheme is proposed, and a specialization is defined for each of the three forms of measurement corruption. Abstract conditions are obtained under which the parameter vector estimate converges to a neighborhood of the true parameter vector. Application of these conditions is illustrated through the use of a Long Observation Time analysis.