On the choice of uncertainty structure in identification for robust control

Various techniques of system identification exist providing for a nominal model and uncertainty bound. An important question is what the implications are for the particular choice of the structure in which the uncertainty is described when dealing with robust stability/performance analysis of a given controller and when dealing with robust synthesis. An amplitude-bounded (circular) uncertainty set can equivalently be described in terms of an additive, Youla parameter and ν-gap uncertainty. Closed-loop performance functions based on these sets are again bounded by circles in the frequency domain, allowing for exact worst-case performance calculation and for the evaluation of the consequences of uncertainty for robust design.