We summarize the main points that we have tried to make, and we discuss some
applications and extensions of the methods described in this book, as well as some
history of the main ideas.
16.1
The Main Points
An explicit framework. A sensible formulation of the controller design problem
is possible only by considering simultaneously all of the closed-loop transfer
functions of interest, i.e., the closed-loop transfer matrix , which should
H
include every closed-loop transfer function necessary to evaluate a candidate
design.
Convexity of many specications. The set of transfer matrices that meet a
design speci cation often has simple geometry|a ne or convex. In many
other cases it is possible to form convex inner (conservative) approximations.
Eectiveness of convex optimization. Many controller design problems can
be cast as convex optimization problems, and therefore can be \e ciently"
solved.
Numerical methods for performance limits. The methods described in this
book can be used both to design controllers (via the primal problem) and to
nd the limits of performance (via the dual problem).
16.2
Control Engineering Revisited
In this section we return to the broader topic of control engineering. Some of the
major tasks of control engineering are shown in gure 16.1:
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