Models developed from first principles often contain coefficients that
are nonlinear functions of design parameters, which themselves are ge
nerally only known within some tolerance. Analysis and design of contr
ollers for such models (plants) are often expedited through the use of
an overbounding interval plant representation of the original plant.
However, such representations are known to introduce conservativeness.
As an alternative, we provide an algorithm for synthesizing a frequen
cy-dependent convex hull approximation of an uncertain plant with nonl
inear coefficients, which we refer to as a minimized plant. We develop
several theorems that demonstrate reduced conservativeness through th
e use of minimized plants. In particular, the use of these plants to d
etermine robust stability margins results in an improvement over the u
se of overbounding interval plants. We also illustrate in an example h
ow a constant coefficient compensator and minimized plant meet a given
set of design specifications, but the same compensator fails to meet
specifications when analysed using an interval plant. As reduced conse
rvativeness simplifies the design process, the convex hull synthesis a
lgorithm and associated theorems provided in this paper facilitate rob
ust controller analysis and design.