Nominal and Robust Loop Shaping

In this paper, classical frequency-response multivariable comnpensator design is studied. This problem consists of chosing a linear controller which gives the sensitivity and complementary sensitivity functions desirable properties. The problem is given two formulations as optimal multivariable stability margin (km) synthesis (or ¿-synthesis, robustness margin synthesis) problems, thereby establishing the consistency with and unification of the present problem with modern robust control theory. These formulations are termed the nominal and the robust loop shaping problems. A quantitative assessment of how well the standard H^¿-theory performs in this context is given for the multivariable case, using new bounds. The primary conclusion is that the existing H^¿-theory does surprisingly well in handling multivariable problems with classical frequency response specifications.