A note on H∞ system identification with probabilistic apriori information

This paper presents an analysis of H_∞ system identification where the apriori information given on the unknown system to be identified is described probabilistically. The H_∞ system identification problem concerns the construction of a linear shift invariant exponentially stable system from a combination of apriori and experimental information. The goal is to construct both a nominal system and an explicit quantification of model uncertainty in the H_∞ norm utilising the apriori and experimental information. The experimental information assumed available in this paper is a set of corrupted point frequency estimates of the unknown system. The apriori information consists of a probability measure specifying the probability of bonds on the norm of the derivative of the unknown system. The problem formulation tion is given for this probabilistic setting with the error criterion allowing a probabilistic tolerance of identification to be given. it is shown that the probabilistic H_∞ problem is equivalent to a worst case problem that is constructed from the probabilistic one. This construction allows near optimal algorithms to be constructed for the probabilistic H_∞, identification problem.