Seron M.M., Braslavsky J.H., Goodwin G.C. Fundamental Limitations in Filtering and Control

Springer, 2016. — 384 p.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 relative 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 accompanied 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 non-minimum phase zeros.
The original motivation for the study of fundamental limitations in feedback was control system design. However, it has been recently realized that similar constraints hold for many related problems including filtering and fault detection. To give the flavor of the filtering results, consider the frequently quoted problem of an inverted pendulum. It is well known that this system is completely observable from measurements of the carriage position. What is less well known is that it is fundamentally difficult to estimate the pendulum angle from measurements of the carriage position due to the location of open-loop non-minimum phase zeros and unstable poles. Minimum sensitivity peaks of 40 dB are readily predictable using Poisson integral type formulae without needing to carry out a specific design. This clearly suggests that a change in the instrumentation is called for, i.e., one should measure the angle directly. We see, in this example, that the fundamental limitations point directly to the inescapable nature of the difficulty and thereby eliminate the possibility of expending effort on various filter design strategies that we know, ab initio, are doomed to failure.
Recent developments in the field of fundamental design limitations include extensions to multivariable linear systems, sampled-data systems, and nonlinear systems.
At this point in time, a considerable body of knowledge has been assembled on the topic of fundamental design limitations in feedback systems. It is thus timely to summarize the key developments in a modern and comprehensive text. This has been our principal objective in writing this book. We aim to cover all necessary background and to give new succinct treatments of Bode's original work together with all contemporary results.Part I Introduction
A Chronicle of System Design Limitations
Part II Limitations in Linear Control
Review of General Concepts
SISO Control
MIMO Control
Extensions to Periodic Systems
Extensions to Sampled-Data Systems
Part III Limitations in Linear Filtering
General Concepts
SISO Filtering
MIMO Filtering
Extensions to SISO Prediction
Extensions to SISO Smoothing
Part IV Limitations in Nonlinear Control and Filtering
Nonlinear Operators
Nonlinear Control
Nonlinear Filtering
Part V Appendices
A: Review of Complex Variable Theory
B: Proofs of Some Results in the Chapters
C: The Laplace Transform of the Prediction Error
D: Least Squares Smoother Sensitivities for Large τ