42 CHAPTER 2. OVERVIEWOF THE UNDERLYING THEORY
Figure 2.8: Closed loop system, G(s), for performance analysis
initial choice of γfor the H∞design procedure. We will see later (Section 2.5) that it
can also be used to initialize the D-Kiteration procedure when an open-loop H∞design
is poorly conditioned.
2.4 µAnalysis2.4.1 Measures of Performance
Section 2.3 presented design performance objectives in terms of the norm (H2or H∞)of
a closed loop system. We will now expand on this idea of performance. Considerthe
closed loop system illustrated in Figure 2.8. The interconnection structure, P(s), is
specified such that wrepresents unknown inputs; typically reference commands,
disturbances and noise. The outputs, e, represent signals that we would like to be small.
“Small” means in the sense of a selected norm. These signals might include actuator
effort, and tracking error. As Figure 2.8 suggests, this analysis is typically applied after
calculating a controller.
The inputs ware described only as members of a set. The performance question is then:
For al l winthis set, are all possible outputs ealso in some set? The following set