What Norm Should One Use in Mixed Sensitivity Minimization

摘要

In the mixed sensitivity minimization problem one minimizes some weightedcombination of the sensitivity function S and the complementary sensitivity function 1-S. Depending on the norm that one uses, one gets different results. In the discrete case one may use, e.g., an l(sup infinity symbol)-norm (maximal deviation is minimized), an l(sup 2)-norm (the energy of the output is minimized), or an l(sup 1)-norm (the total mass of the output is minimized). Here the authors concentrate on the l(sup infinity symbol) and l(sup 1)-cases. The authors show that in these cases there are several competing norms that all make sense. In particular, the solution is sensitive to the interpretation of the problem as a multi input single output problem or as a single input multi output problem. The authors present a number of such norms, and investigate how the solution changes with the norm.