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 Lorenzo Farina 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 the Leontief 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 and Applications an indispensable resource for researchers andprofessionals in a broad range of fields.
Table of Content
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.
About the author
LORENZO FARINA, Ph D, is Associate Professor of Modeling and Simulation, Dipartimento di Informatica e Sistemistica, Universita di Roma ‘La Sapienza, ‘ Italy. SERGIO RINALDI, Ph D, is Full Professor of Systems Theory, Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy.
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