MIXED H-2/H-INFINITY

In this paper vie consider the problem of minimizing a nominal H-2 performance measure subject to robust stability constraints for systems having multiple operating points. Performance is measured in terms of a weighted sum of the individual H-2 norms at each plant condition, whereas robust stability is enforced through H-infinity-norm bounds. The problem is solved by considering a new time-domain scalar cost function 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 problem that, for t(f) --> infinity, recovers the original objective of minimizing the performance measure subject to the given H-infinity bounds. The resulting optimization problem is smooth, and hence standard gradient-based software can be applied. Moreover, this formulation allows for the synthesis of linear time-invariant controllers having a prespecified order and structure. The method is illustrated by the design of a single first-order controller for the pitch stability augmentation system of an F-15 aircraft operating at both subsonic and supersonic flight conditions.