Description
Book SynopsisThis volume introduces the reader to the world of positive linear systems, an important and fascinating class of linear systems. The subject matter is divided into three parts, including definitions and basic properties of liner systems, theoretical results, and the study of some classes of positive linear systems relevant in applications.
Trade Review"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)
Table of ContentsDEFINITIONS.
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.
