Introduction to Mathematical Systems Theory : A Behavioral Approach (Texts in Applied Mathematics, Vol. 26) [Hardcover]

Jan Willem Polderman (Author), Jan C. Willems (Author)

Book Description

Publication Date: November 7, 1997 | ISBN-10: 0387982663 | ISBN-13: 978-0387982663 | Edition: 1

Using the behavioural approach to mathematical modelling, this book views a system as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. The first part analyses the structure of the set of trajectories generated by such dynamical systems, and derives the conditions for two systems of differential equations to be equivalent in the sense that they define the same behaviour. In addition the memory structure of the system is analysed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. In the third part, control problems are considered, in particular stabilisation and pole placement questions. Suitable for advanced undergraduate or beginning graduate students in mathematics and engineering, this text contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.

Editorial Reviews

Review

From the reviews: INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL "The present book is a major original contribution to the literature and is of high quality. The most original chapters are the ‘strongly behavioural’ Chapters 1-6 and the historical preface. The introduction is carefully written and each chapter ends with a precise recapitulation of what has been done. It is well organized, technically well written, philosophically nice, and contains a wealth of examples and exercises. It is also well self-contained for its audience…scientific honesty dictates to congratulate the authors and to recommend this book as a textbook to a large public of systems and control students, and especially for those having already followed a first course on linear systems."

Product Details

• Hardcover: 424 pages
• Publisher: Springer; 1 edition (November 7, 1997)
• Language: English
• ISBN-10: 0387982663
• ISBN-13: 978-0387982663
• Product Dimensions: 9.5 x 6.4 x 1.2 inches
• Shipping Weight: 1.7 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,459,795 in Books (See Top 100 in Books)

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4 of 4 people found the following review helpful:

5.0 out of 5 stars Systems theory done right!, April 6, 2004

By A Customer

This review is from: Introduction to Mathematical Systems Theory : A Behavioral Approach (Texts in Applied Mathematics, Vol. 26) (Hardcover)

This is an excellent book on mathematical control theory. As opposed to the classical state-space approach, the behavioural theory gives a more fundamental and natural way of looking at physical systems. The book deals with the notions of controllability, observability, stability and feedback in a beautiful mathematical framework. A more appropriate title would be "Systems theory done right"!

5.0 out of 5 stars First Aid to those outside the EE community, December 2, 2006

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This review is from: Introduction to Mathematical Systems Theory : A Behavioral Approach (Texts in Applied Mathematics, Vol. 26) (Hardcover)

The book starts off with an extremely useful modeling term: "Exclusion Law." This term describes a notion that any closed system of physical laws/equations (Newton's, etc.) state what's included (possible) and what's excluded (impossible) from its (a certain set of physical laws/equations) interpretation of reality.

Most of the concepts in this text will be nothing new to those who already have a bachelor of science in electrical engineering. Still, learning from the author's choice of words and his arrangement of materials will provide one with a very effective way of communicating modeling ideas to those outside the EE community or to those who are somehow academically juvenile (for example, speaking with someone who had to suffer a poor signals and systems instructor or with anyone who had to deal with a similar academic situation).

Here's a quote from page 12:

"Now it becomes necessary to consider two cases:"

From page 1:

"We view a mathematical model as an exlcusion law. A mathematical model expresses the OPINION that some things can happen, are possible, while others cannot, are declared impossible. Thus Kepler claims that planetary orbits that do not satisfy his three famous laws are impossible. In particular, he judges nonelliptical orbits as unphysical. ... Economic production functions tell us that certain amounts of raw materials, capital, and labor are needed in order to manufacture a finished product: it prohibits the creation of finished products unless the required resources are available."

And from page 8:

"Dynamical Systems.... The adjective dynamical refers to phenomena with a delayed reaction, phenomena with an aftereffect, with transients, oscillations, and, perhaps, an approach to equilibrium. ...a mathematical model in which the objects of interest are functions of time..."