In part I, A Framework for Controller Design, we develop a formal framework for
many of the concepts described above: the system to be controlled, the control con-
guration, the controller, and the design goals and objectives for controller design.
In part II, Analytical Tools, we rst describe norms of signals and systems, which
can be used to make precise such design goals as \error signals should be made small,
while the actuator signals should not be too large". We then study some important
geometric properties that many controller design speci cations have, and introduce
the important notion of a closed-loop convex design speci cation.
In part III, Design Specications, we catalog many closed-loop convex design
speci cations. These design speci cations include speci cations on the response of
the closed-loop system to the various commands and disturbances that may act on
it, as well as robustness speci cations that limit the sensitivity of the closed-loop
system to changes in the system to be controlled.
In part IV, Numerical Methods, we describe numerical methods for solving the
controller design problem. We start with some controller design problems that have
analytic solutions, i.e., can be solved rapidly and exactly using standard methods.
We then turn to the numerical solution of controller design problems that can be
expressed in terms of closed-loop convex design speci cations, but do not have
analytic solutions.
In the nal chapter we give some discussion of the methods described in this
book, as well as some history of the main ideas.
1.5.1