In this paper vie consider the problem of minimizing a nominal H-2 per
formance measure subject to robust stability constraints for systems h
aving multiple operating points. Performance is measured in terms of a
weighted sum of the individual H-2 norms at each plant condition, whe
reas robust stability is enforced through H-infinity-norm bounds. The
problem is solved by considering a new time-domain scalar cost functio
n J(infinity) (t(f)) that incorporates the H-infinity constraints into
a single cost function. Using the proposed formulation, the mixed H-2
/H-infinity design problem becomes an unconstrained optimization probl
em that, for t(f) --> infinity, recovers the original objective of min
imizing the performance measure subject to the given H-infinity bounds
. The resulting optimization problem is smooth, and hence standard gra
dient-based software can be applied. Moreover, this formulation allows
for the synthesis of linear time-invariant controllers having a presp
ecified order and structure. The method is illustrated by the design o
f a single first-order controller for the pitch stability augmentation
system of an F-15 aircraft operating at both subsonic and supersonic
flight conditions.