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Positive Linear Systems. Theory and Applications. Edition No. 1. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts

  • ID: 2181118
  • Book
  • July 2000
  • 318 Pages
  • John Wiley and Sons Ltd
A complete study on an important class of linear dynamicalsystems-positive linear systems

One of the most often-encountered systems in nearly all areas ofscience and technology, positive linear systems is a specific butremarkable and fascinating class. Renowned scientists LorenzoFarina and Sergio Rinaldi introduce readers to the world ofpositive linear systems in their rigorous but highly accessiblebook, rich in applications, examples, and figures.

This professional reference is divided into three main parts: Thefirst part contains the definitions and basic properties ofpositive linear systems. The second part, following the theoreticalexposition, reports the main conceptual results, consideringapplicable examples taken from a number of widely used models. Thethird part is devoted to the study of some classes of positivelinear systems of particular relevance in applications (such as theLeontief model, the Leslie model, the Markov chains, thecompartmental systems, and the queueing systems). Readers familiarwith linear algebra and linear systems theory will appreciate theway arguments are treated and presented.

Extraordinarily comprehensive, Positive Linear Systemsfeatures:

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 systemstheory for readers unfamiliar with the mathematics used

Farina and Rinaldi make no effort to hide their enthusiasm for thetopics presented, making Positive Linear Systems: Theory andApplications an indispensable resource for researchers andprofessionals in a broad range of fields.
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DEFINITIONS.

Definitions and Conditions of Positivity.

Influence Graphs.

Irreducibility, Excitability and Transparency.

PROPERTIES.

Stability.

Spectral Characterization of Irreducible Systems.

Positivity of Equilibria.

Reachability and Observability.

Realization.

Minimum Phase.

Interconnected Systems.

APPLICATIONS.

Input-Output Analysis.

Age-Structured Population Models.

Markov Chains.

Compartmental Systems.

Queueing Systems.

Conclusions.

Annotated Bibliography.

Bibliography.

Appendices.

Index.
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Lorenzo Farina University of Rome, La Sapienza, Italy.

Sergio Rinaldi Politecnico di Milano, Italy.
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