##
**Positive linear systems. Theory and applications.**
*(English)*
Zbl 0988.93002

New York, NY: Wiley. ix, 305 p. (2000).

This nice book about positive linear systems is written with enthusiasm. On a theoretical level it gives in an input-state-output framework various definitions, characterizations and properties of positive linear systems.

Some key words are: influence graphs, stability, spectral characterization, reachability and observability and realization. So the authors also give a nice introduction to the nonnegative realization problem.

After the first hundred pages about the theory, a chapter of about seventy pages follows with applications to input-output analysis, age-structured population models, Markov chains, compartmental systems and queuing systems.

The book contains a useful annotated bibliography and two appendices, one about linear algebra and matrix theory and another about linear systems theory.

Therefore this book is rather selfcontained.

The style is rather informal but not unprecise, and the authors really succeed in conveying their enthusiasm and the flavor of the subject.

The reviewer therefore considers this book to be a welcome introduction and addition to the theory and applications of positive linear systems.

Some key words are: influence graphs, stability, spectral characterization, reachability and observability and realization. So the authors also give a nice introduction to the nonnegative realization problem.

After the first hundred pages about the theory, a chapter of about seventy pages follows with applications to input-output analysis, age-structured population models, Markov chains, compartmental systems and queuing systems.

The book contains a useful annotated bibliography and two appendices, one about linear algebra and matrix theory and another about linear systems theory.

Therefore this book is rather selfcontained.

The style is rather informal but not unprecise, and the authors really succeed in conveying their enthusiasm and the flavor of the subject.

The reviewer therefore considers this book to be a welcome introduction and addition to the theory and applications of positive linear systems.

Reviewer: Johannes W.Nieuwenhuis (Groningen)

### MSC:

93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |

93C05 | Linear systems in control theory |

93C95 | Application models in control theory |

93B15 | Realizations from input-output data |

93D20 | Asymptotic stability in control theory |

93B03 | Attainable sets, reachability |