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Rafael Bru and Sergio Romero-Vivó (Eds.) Lecture Notes in Control and Information Sciences 389 Editors: M. Thoma, F. Allgöwer, M. Morari Rafael Bru and Sergio Romero-Vivó (Eds.) Positive Systems Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 2009) Valencia, Spain, September 2–4, 2009 ABC Series Advisory Board P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis Editors Rafael Bru Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camí de Vera s/n, 46022 Valencia Spain E-mail: [email protected] Sergio Romero-Vivó Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camí de Vera s/n, 46022 Valencia Spain E-mail: [email protected] ISBN 978-3-642-02893-9 e-ISBN 978-3-642-02894-6 DOI 10.1007/978-3-642-02894-6 Lecture Notes in Control and Information Sciences ISSN 0170-8643 Library of Congress Control Number: Applied for c 2009 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed in acid-free paper 543210 springer.com Preface Nowadays, the researchers into Control Theory and its Applications as well as Matrix Analysis are well aware and recognize the importance of Positive Sys- tems. This volume contains the proceedings of the “Third Multidisciplinary Symposium on Positive Systems: Theory and Applications (POSTA09)” held in Valencia, Spain, September 2–4, 2009. At present, this is the only world congress whose main topic is focused on this field. After this third event, we think that we have established the basis of a regular triennial event supported in the task of the previous organizing committees and hope to have met the requirements of their expectations. This POSTA09 meeting has been organized by members of the “Univer- sitat Polit`ecnica de Val`encia”,who have taken their doctor’s degree in the subjects of the conference. We are grateful to all of them for their enthu- siasm, effort and especially their collaboration, without the help of which the outcome would have never been the same. Also, we highly appreciate Christian Commault for having his experience at our disposal. Besides that, we wish to thank the International Programme Committee components and additional referees for their outstanding work in the review process of the contributions. We are happy to say that their constructive suggestions and positive comments have improved the quality of the presentations. We are very much obliged to the following organizations for having fi- nancially backed this congress: “Ministerio de Educaci´on y Ciencia”, “Con- selleria d’Educaci´o de la Generalitat Valenciana”, “Universitat Polit`ecnica de Val`encia (UPV)” and “Sociedad Espa˜nola de Matem´atica Aplicada (SEMA)”. We extend our gratitude to the “International Linear Algebra Society (ILAS)”, “Institut Universitari de Matem`atica Multidisciplin`aria (IMM)” and the “Algebra´ Lineal, An´alisis Matricial y Aplicaciones (ALAMA)” network for having endorsed this meeting. Finally, we would like to thank all of the par- ticipants for their attendance in spite of these hard times. Their presence here reasserts the success of this conference and we hope to see them successively in the future. Valencia, Rafael Bru September 2009 Sergio Romero-Viv´o Organization Program Committee Chairman Rafael Bru Universitat Polit`ecnica de Val`encia, Spain Members Georges Bastin Universit´e Catholique de Louvain, Belgium Luca Benvenuti Universit`a di Roma “La Sapienza”, Italy Vincent Blondel Universit´e Catholique de Louvain, Belgium Rafael Cant´o Universitat Polit`ecnica de Val`encia, Spain Carmen Coll Universitat Polit`ecnica de Val`encia, Spain Bart De Moor Katholieke Universiteit Leuven, Belgium Alberto De Santis Universit`a di Roma “La Sapienza”, Italy Elena De Santis Universit`a dell’Aquila, Italy Lorenzo Farina Universit`a di Roma “La Sapienza”, Italy Stephane Gaubert INRIA, Ecole Polytechnique, France Alessandro Giua Universit`a di Cagliari, Italy Jean-Luc Gouz´e INRIA Sophia Antipolis, France Diederich Hinrichsen Universit¨at Bremen, Germany Tadeusz Kaczorek Warsaw University of Technology, Poland Ulrich Krause Universit¨at Bremen, Germany Volker Mehrmann Technische Universit¨at Berlin, Germany Ventsi Rumchev Curtin University of Technology, Australia Maria Pia Saccomani Universit`a di Padova, Italy Elena S´anchez Universitat Polit`ecnica de Val`encia, Spain Jan H. van Schuppen CWI, Amsterdam, The Netherlands Robert Shorten The Hamilton Institute, Co. Kildare, Ireland Anton A. Stoorvogel University of Twente, The Netherlands VIII Organization Ana M. Urbano Universitat Polit`ecnica de Val`encia, Spain Maria Elena Valcher Universit`a di Padova, Italy Paul Van Dooren Universit´e Catholique de Louvain, Belgium Joseph Winkin Universit´e Notre-Dame de la Paix, Belgium Organizing Committee Bego˜na Cant´o Universitat Polit`ecnica de Val`encia, Spain Rafael Cant´o Universitat Polit`ecnica de Val`encia, Spain Beatriz Ricarte Universitat Polit`ecnica de Val`encia, Spain Sergio Romero-Viv´o Universitat Polit`ecnica de Val`encia, Spain Additional Referees Esteban Bailo Maya Mincheva Gregory Batt Francisco Pedroche Bego˜na Cant´o Juan Manuel Pe˜na Bart De Schutter Harish Pillai Zong Woo “Victor” Geem Beatriz Ricarte Josep Gelonch Sergio Romero-Viv´o Bernd Heidergott Bartek Roszak Julien Hendrickx Boris Shapiro On´esimo Hern´andez-Lerma HalL.Smith Alexandros Karatzoglou Juan Ramon Torregrosa Jerzy Klamka Elena Virnik Thomas G. Kurtz Yimin Wei Hongwei Lin Eva Zerz James H. Liu Contents Plenary Talks Reputation Systems and Nonnegativity ...................... 3 Cristobald de Kerchove, Paul Van Dooren Lyapunov Exponents and Uniform Weak Normally Repelling Invariant Sets ..................................... 17 Paul Leonard Salceanu, Hal L. Smith Reachability Analysis for Different Classes of Positive Systems ..................................................... 29 Maria Elena Valcher Invited Sessions On the Positive LQ-Problem for Linear Discrete Time Systems ..................................................... 45 Charlotte Beauthier, Joseph J. Winkin The Importance of Being Positive: Admissible Dynamics for Positive Systems ......................................... 55 Luca Benvenuti, Lorenzo Farina Detectability, Observability, and Asymptotic Reconstructability of Positive Systems ....................... 63 Tobias Damm, Cristina Ethington Stability Radii of Interconnected Positive Systems with Uncertain Couplings ......................................... 71 Diederich Hinrichsen X Contents Linear Operators Preserving the Set of Positive (Nonnegative) Polynomials .................................. 83 Olga M. Katkova, Anna M. Vishnyakova Convergence to Consensus by General Averaging ............ 91 Dirk A. Lorenz, Jan Lorenz Stability and D-stability for Switched Positive Systems ...... 101 Oliver Mason, Vahid S. Bokharaie, Robert Shorten On Positivity and Stability of Linear Volterra-Stieltjes Differential Systems ......................................... 111 Pham Huu Anh Ngoc Eigenvalue Localization for Totally Positive Matrices ........ 123 Juan Manuel Pe˜na Positivity Preserving Model Reduction ...................... 131 Timo Reis, Elena Virnik The Minimum Energy Problem for Positive Discrete-Time Linear Systems with Fixed Final State ....................... 141 Ventsi Rumchev, Siti Chotijah A Rollout Algorithm for Multichain Markov Decision Processes with Average Cost ................................ 151 Tao Sun, Qianchuan Zhao, Peter B. Luh Analysis of Degenerate Chemical Reaction Networks ........ 163 Markus Uhr, Hans-Michael Kaltenbach, Carsten Conradi, J¨org Stelling k-Switching Reachability Sets of Continuous-Time Positive Switched Systems............................................ 173 Maria Elena Valcher Contributed Papers Inverse-Positive Matrices with Checkerboard Pattern ........ 185 Manuel F. Abad, Mar´ıa T. Gass´o, Juan R. Torregrosa Some Remarks on Links between Positive Invariance, Monotonicity, Strong Lumpability and Coherency in Max-Plus Algebra ........................................... 195 Mourad Ahmane, Laurent Truffet Contents XI Stability Analysis and Synthesis for Linear Positive Systems with Time-Varying Delays .......................... 205 Mustapha Ait Rami Linear Programming Approach for 2-D Stabilization and Positivity .................................................... 217 Mohammed Alfidi, Abdelaziz Hmamed, Fernando Tadeo An Algorithmic Approach to Orders of Magnitude in a Biochemical System ......................................... 233 Eric Benoˆıt, Jean-Luc Gouz´e Structural Identifiability of Linear Singular Dynamic Systems ....................................................
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