In this chapter we consider in detail performance specications, which limit the
response of the closed-loop system to the various commands and disturbances
that may act on it. We show that many of these performance specications are
closed-loop convex.
We organize our discussion of performance speci cations by their meaning or pur-
pose (in the context of controller design), and not by the mathematical form of
the constraints. In fact we shall see that performance speci cations with di erent
meanings, such as a limit on errors to commands, a minimum acceptable level of
regulation, and a limit on actuator e ort, can be expressed in similar forms as lim-
its on the size of a particular submatrix of the closed-loop transfer matrix . For
H
this reason our discussion of these types of speci cations will become briefer as the
chapter progresses and the reader can refer back to chapter 5 or other speci cations
that have a similar form.
To facilitate this organization of performance speci cations by meaning, we par-
tition the exogenous input vector as follows:
w
2
c 3
c
commands
= w
l
n
4
d 5
d disturbances
w
l
n
w
etc
other components of
w
w
The c components of c are the command, reference, or set-point signals|the
n
w
\input" in classical control terminology. The d components of d are the dis-
n
w
turbance or noise signals. The vector signal etc contains all remaining exogenous
w
inputs|some of these signals will be discussed in chapter 10.
We partition the regulated variables:
2
c 3
c
commanded variables
z
l
n
= 6 a 7
a actuator signals
z
l
n
6
7
z
4
o 5
o other critical signals
z
l
n
etc
other components of
z
z
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