Mathematical Control Theory: An Introduction (Systems & Control: Foundations & Applications) 2nd Edition by Jerzy Zabczyk (PDF)

Description

This textbook presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus.In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems.This second edition includes new chapters that introduce a variety of topics, such as controllability with vanishing energy, boundary control systems, and delayed systems. With additional proofs, theorems, results, and a substantially larger index, this new edition will be an invaluable resource for students and researchers of control theory.Mathematical Control Theory: An Introduction will be ideal for a beginning graduate course in mathematical control theory, or for self-study by professionals needing a complete picture of the mathematical theory that underlies the applications of control theory.From reviews of the first edition:At last! We did need an introductory textbook on control which can be read, understood, and enjoyed by anyone. Gian-Carlo Rota, The Bulletin of Mathematics BooksIt covers a remarkable number of topics…The exposition is excellent, and the book is a joy to read. A novel one-semester course covering both linear and nonlinear systems could be given…The book is an excellent one for introducing a mathematician to control theory. Bulletin of the AMSIndeed, for mathematicians who look for the basic ideas or a general picture about the main branches of control theory, I believe this book can provide an excellent bridge to this area. IEEE Control Systems Magazine

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I am a salesman and a ‚hobby mathematician‘, so please take my comments with this in mind.The first three chapters on control theory in R^n are clear.The proofs of the theorems, propositions, etc are easy to follow, the gaps are rarely so large that I needed paper and pencil to fill them. I believe a undergraduate background in math is sufficient to understand everything.Chapter IV on infinite dimensional systems is completely different.Yes, the background needed is much more, as these systems apparently ‚live‘ in Hilbert spaces. The frustrating point is, that the author seems to change the background required constantly. 15 lines of simple inequalities are followed by ‚it is easy to see that A is dense in B‘. Is it really ‚easy to see‘ and I am just too dumb – or can‘t the author be bothered to explain?The situation is not helped by the fact that book is fully of misprints. I found over 60 of them, many of them not harmless – and surely I only found a small percentage.Small, but annoying is that theorems, lemmas, propositions, corollaries all have their own numbering systems, so theorem 3.14 may well be before proposition 3.5. This makes finding them a bit more time consuming.So, while I enjoyed chapters I – III, chapter IV was a very frustrating experience.

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