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Positive Linear Systems: Theory and Applications

ISBN: 978-0-471-38456-4
318 pages
July 2000
Positive Linear Systems: Theory and Applications (0471384569) cover image
A complete study on an important class of linear dynamical systems-positive linear systems

One of the most often-encountered systems in nearly all areas of science and technology, positive linear systems is a specific but remarkable and fascinating class. Renowned scientists Lorenzo Farina and Sergio Rinaldi introduce readers to the world of positive linear systems in their rigorous but highly accessible book, rich in applications, examples, and figures.

This professional reference is divided into three main parts: The first part contains the definitions and basic properties of positive linear systems. The second part, following the theoretical exposition, reports the main conceptual results, considering applicable examples taken from a number of widely used models. The third part is devoted to the study of some classes of positive linear systems of particular relevance in applications (such as the Leontief model, the Leslie model, the Markov chains, the compartmental systems, and the queueing systems). Readers familiar with linear algebra and linear systems theory will appreciate the way arguments are treated and presented.

Extraordinarily comprehensive, Positive Linear Systems features:
* Applications from a variety of backgrounds including modeling, control engineering, computer science, demography, economics, bioengineering, chemistry, and ecology
* References and annotated bibliographies throughout the book
* Two appendices concerning linear algebra and linear systems theory for readers unfamiliar with the mathematics used

Farina and Rinaldi make no effort to hide their enthusiasm for the topics presented, making Positive Linear Systems: Theory and Applications an indispensable resource for researchers and professionals in a broad range of fields.
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Definitions and Conditions of Positivity.

Influence Graphs.

Irreducibility, Excitability and Transparency.



Spectral Characterization of Irreducible Systems.

Positivity of Equilibria.

Reachability and Observability.


Minimum Phase.

Interconnected Systems.


Input-Output Analysis.

Age-Structured Population Models.

Markov Chains.

Compartmental Systems.

Queueing Systems.


Annotated Bibliography.



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LORENZO FARINA, PhD, is Associate Professor of Modeling and Simulation, Dipartimento di Informatica e Sistemistica, Universita di Roma "La Sapienza," Italy. SERGIO RINALDI, PhD, is Full Professor of Systems Theory, Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy.
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"Explores a class of linear dynamical systems called positive linear systems whose state variables take only non-negative values." (SciTech Book News,Vol. 24, No. 4, December 2000)

"The exposition of the topics is consistent and clear. The book is addressed to graduate students, scientists and engineers in control." (Mathematical Reviews, Issue 2001g)

"This book gives an interesting overview of results regarding single-input single-output, time-invariant, finite-dimensional linear poitive systems." (Mathematical Reviews, 2001g:93001)

"There are lots of things to like about this book. In particular, I liked the appendix on element so f linear systems theory.... Then there is the clear enthusiasm of the authors for the subject...useful for self study or as a supplement in a more advanced course..." (SIAM Review, Vol. 43, No. 3)

"Very well-written and well-organized suitable for students who have had a first course in differential equations." (American Mathematical Monthly, January 2002)

"...the authors really succeed in conveying their enthusiasm and the flavor of the subject..." (Zentralblatt Math, Vol.988, No.13, 2002)
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