Robust performance analysis for a range of frequencies

Time domain specifications such as overshoot, rise time and tracking behaviour can be extracted from an amplitude frequency response. For uncertain systems we use for this an upper bound on the maximum amplitude frequency response. There are tools which can compute this upper bound for each frequency in a grid. Computing this upper bound can be computational expensive when studying a large scale system hence it is interesting to have a low dense frequency grid. However, in such a case, it can for example occur that the maximum peak of the amplitude frequency response occurs at a frequency which is not in this grid. A consequence is that the overshoot will not be determined well for the system. In this paper we will present a method such that this can not occur. We will augment the uncertainty set with an additional uncertain parameter. This uncertain parameter will cover the frequencies which are not covered by the grid. This allows us to do a robustness analysis for a range of frequencies. In this case we are sure that we do not miss any crucial information with respect to the amplitude frequency response lying in between the frequencies in the grid. We illustrate this using two simulation examples.