Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches
by Dan Simon, Published by Wiley
ISBN 0-471-70858-5, hardback, 552 pp, $95.00
EN-Genius Reviewer: Dennis L. Feucht

As electronics becomes more sophisticated, control theory moves closer to the essential center of what an engineer must know to design leading-edge products or processes. Power electronics in particular is a fertile ground for the application of advanced control techniques. This book, by an EE professor and control theorist at Cleveland State Uuniversity in Ohio and NASA consultant with extensive industrial experience, is a good place to begin in gaining an engineering-level understanding of the more settled areas of advanced control. In particular, one area of control that has grown into a sub-specialty has to do with the feedback of output and system state variables to the controller -- the H block in the classic feedback diagram, as it were. In the presence of noise and an inability to observe as much of what is going on as desired, these techniques can be essential, and are referred to as estimation.

This book is loaded with matrix mathematics, yet the style of presentation builds logically, one understandable step at a time. Simon has good didactic form, in trying to make sure that he is not assuming what the reader does not know but must in order to understand the flow of the presentation.

The introduction of the book shows which chapters one must understand to comprehend other chapters. The beginning chapters lay the basic theoretical foundation in linear systems theory. Chapter 1 contains a quick but well-presented survey of the later-used matrix math, how the basic linear system description is formulated, and then some numerical methods for its application on computers: rectangular, trapezoidal, and Runga-Kutta integration. Basic control concepts of observability, controllability, and stability are introduced.

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