Bhattacharyya S., Datta A., Keel L. Linear Control Theory: Structure, Robustness and Optimization

CRC Press, 2009. — 930 p.Successfully classroom-tested at the graduate level, Linear Control Theory: Structure, Robustness, and Optimization covers three major areas of control engineering (PID control, robust control, and optimal control). It provides balanced coverage of elegant mathematical theory and useful engineering-oriented results.The first part of the book develops results relating to the design of PID and first-order controllers for continuous and discrete-time linear systems with possible delays. The second section deals with the robust stability and performance of systems under parametric and unstructured uncertainty. This section describes several elegant and sharp results, such as Kharitonov’s theorem and its extensions, the edge theorem, and the mapping theorem. Focusing on the optimal control of linear systems, the third part discusses the standard theories of the linear quadratic regulator, Hinfinity and l1 optimal control, and associated results.Written by recognized leaders in the field, this book explains how control theory can be applied to the design of real-world systems. It shows that the techniques of three term controllers, along with the results on robust and optimal control, are invaluable to developing and solving research problems in many areas of engineering.Part I constitute a modernized version of Classical Control Theory appropriate
to the computer-aided design environment of the 21st century.
In Part II we deal with the Robust Stability and Performance of systems
under parametric as well as unstructured uncertainty. Several elegant and
sharp results such as Kharitonov’s Theorem and its extensions, the Edge
Theorem and the Mapping Theorem are described. The main thrust of the
results is to reduce the verification of stability and performance over the entire
uncertainty set to certain extremal test sets, which are points or lines. These
results are useful to engineers as aids to robustness analysis and synthesis of
control systems.
Part III deals with Optimal Control of linear systems. We develop the stan-
dard theories of the Linear Quadratic Regulator (LQR), H∞ and ℓ1 optimal
control, and associated results. In the LQR chapter we include results on the
servomechanism problem.
We have been using this material successfully in a second graduate level
course in Control Systems for some time. It is our opinion that it gives
a balanced coverage of elegant mathematical theory and useful engineering
oriented results that can serve the needs of a diverse group of students from
Electrical, Mechanical, Chemical, Aerospace, and Civil Engineering as well as
Computer Science and Mathematics. It is possible to cover the entire book in
a 14-week semester with a judicious choice of reading assignments.