Customer Reviews

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

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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"!

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..."