BEYOND SINGULAR-VALUES AND LOOP SHAPES

This paper provides a tutorial look at the status of singular value loop shaping as a paradigm for multivariable feedback design. It shows that this paradigm is effective whenever a design problem's specifications are spatially round, but that it can be arbitrarily conservative otherwise. This happens because singular value conditions for robust performance are not tight (sufficient but not necessary) and can severely overstate actual requirements. An alternate paradigm is discussed that promises to overcome these limitations. This alternative includes a more general problem formulation, a new matrix function mu, and tight conditions for both robust stability and robust performance. The current state of development of this paradigm supports analysis and comparisons of existing feedback designs. To a limited extent, it also supports formal mathematical synthesis of new optimal designs, although much research remains to be done in the synthesis area.