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This book deals with the issue of fundamental limitations in
filtering and control system design. This issue lies at the very
heart of feedback theory since it reveals what is achievable, and
conversely what is not achievable, in feedback systems. The subject
has a rich history beginning with the seminal work of Bode during
the 1940's and as subsequently published in his well-known book
Feedback Amplifier Design (Van Nostrand, 1945). An interesting fact
is that, although Bode's book is now fifty years old, it is still
extensively quoted. This is supported by a science citation count
which remains comparable with the best contemporary texts on
control theory. Interpretations of Bode's results in the context of
control system design were provided by Horowitz in the 1960's. For
example, it has been shown that, for single-input single-output
stable open-loop systems having rela tive degree greater than one,
the integral of the logarithmic sensitivity with respect to
frequency is zero. This result implies, among other things, that a
reduction in sensitivity in one frequency band is necessarily
accompa nied by an increase of sensitivity in other frequency
bands. Although the original results were restricted to open-loop
stable systems, they have been subsequently extended to open-loop
unstable systems and systems having nonminimum phase zeros."
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