H∞ control for competing objectives

The reason [OPT) occurs is simple. Supposr that vou are asked to design a s!stem to optimize a rertain perfornlanre measure at each frequency u. Part of the system i. gi\en and another part, is designable. If the designable part is described by ?i complex var iables f l ( jxj ...,: fx( jG) at f requenq ( j d ) . Then the performance measure is a function r(u.j(w)j for a particular choice of designable 1. Thus the problem of finding the specifications f ( j w ) producing an optimal design is indeed ( O P T ) . If the designable are the stable ?. then E = H"($) or if stabilits of the full system is an issue then a reparametrization usually allows one to take E = H".