To emphasize an aspect of linear controller design that has not been empha-
sized in the past: the determination of limits of performance, i.e., speci ca-
tions that cannot be achieved with a given system and control con guration.
It is not our goal to survey recently developed techniques of linear controller design,
or to (directly) teach the reader how to design linear controllers several existing
texts do a good job of that. On the other hand, a clear formulation of the linear
controller design problem, and an understanding that many of the performance
limits of a linear control system can be computed, are useful to the practicing
control engineer.
Our intended audience includes the sophisticated industrial control engineer, and
researchers and research students in control engineering.
We assume the reader has a basic knowledge of linear systems (Kailath Kai80],
Chen Che84], Zadeh and Desoer ZD63]). Although it is not a prerequisite, the
reader will bene t from a prior exposure to linear control systems, from both the
\classical" and \modern" or state-space points of view. By classical control we refer
to topics such as root locus, Bode plots, PI and lead-lag controllers (Ogata Oga90],
Franklin, Powell, Emami FPE86]). By state-space control we mean the the-
ory and use of the linear quadratic regulator (LQR), Kalman lter, and linear
quadratic Gaussian (LQG) controller (Anderson and Moore AM90], Kwakernaak
and Sivan KS72], Bryson and Ho BH75]).
We have tried to maintain an informal, rather than completely rigorous, approach
to the mathematics in this book. For example, in chapter 13 we consider linear
functionals on in nite-dimensional spaces, but we do not use the term dual space,
and we avoid any discussion of their continuity properties. We have given proofs and
derivations only when they are simple and instructive. The references we cite con-
tain precise statements, careful derivations, more general formulations, and proofs.
We have adopted this approach because we believe that many of the basic ideas
are accessible to those without a strong mathematics background, and those with the
background can supply the necessary quali cations, guess various generalizations,
or recognize terms that we have not used.
A Notes and References section appears at the end of each chapter. We have
not attempted to give a complete bibliography rather, we have cited a few key
references for each topic. We apologize to the many researchers and authors whose
relevant work (especially, work in languages other than English) we have not cited.
The reader who wishes to compile a more complete set of references can start by
computing the transitive closure of ours, i.e., our references along with the references
in our references, and so on.
