Positive Linear Systems (eBook)

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.

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.

"Explores a class of linear dynamical systems called positivelinear systems whose state variables take only non-negativevalues." (SciTech Book News,Vol. 24, No. 4, December 2000)

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

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

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

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

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