Positive Systems: Theory and Applications Proceedings of the First Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 2003), Rome, Italy, August 28-30, 2003

This book contains the proceedings of the First Multidisciplinary International Symposium on Positive Systems Theory and Applications (POSTA 2003) held in Rome, Italy, on August 28-30, 2003. Positive Systems are systems in which the relevant variables assume nonnegative values. These systems are quite common in applications where variables represent positive quantities such as populations, goods, money, time, data packets flowing in a network, densities of chemical species, probabilities etc. The aim of the symposium was to join together researchers working in the different areas related to positive systems such as telecommunications, economy, biomedicine, chemistry and physics in order to provide a multidisciplinary forum where they have the opportunity to exchange ideas and compare results in a unifying framework. Positive Random Systems with Application to Investment....Pages 1-1 Rational Positive Systems for Reaction Networks....Pages 3-5 Min-plus and Max-plus System Theory Applied to Communication Networks....Pages 7-14 Reachability and Invariance Problems in Max-plus Algebra....Pages 15-22 Modelling of Urban Bus Networks in Dioids Algebra....Pages 23-30 Modal Logic and Dioids....Pages 31-38 Monotone Linear Dynamical Systems over Dioids....Pages 39-45 Optimal Control for (max,+)-linear Systems in the Presence of Disturbances....Pages 47-54 Unforced Continuous Petri Nets and Positive Systems....Pages 55-62 Reachability Graph for Autonomous Continuous Petri Nets....Pages 63-70 Modeling Hybrid Positive Systems with Hybrid Petri Nets....Pages 71-78 Simulation and Control of a Bottling Plant using First-order Hybrid Petri Nets....Pages 79-86 Parameter Identifiability of Nonlinear Biological Systems....Pages 87-93 Towards Whole Cell “in Silico” Models for Cellular Systems: Model Set-up and Model Validation....Pages 95-102 Guaranteed Parameter Estimation for Cooperative Models....Pages 103-110 Modeling and Simulation of Genetic Regulatory Networks....Pages 111-118 Qualitative Analysis of Regulatory Graphs: A Computational Tool Based on a Discrete Formal Framework....Pages 119-126 A Reconstruction Algorithm for Gene Regulatory Sparse Networks using Positive Systems....Pages 127-134 The Basic Reproduction Number in a Multi-city Compartmental Epidemic Model....Pages 135-142 Stability Analysis of a Metabolic Model with Sequential Feedback Inhibition....Pages 143-150 Differential Systems with Positive Variables....Pages 151-158 Positivity and Invariance Properties of Nonisothermal Tubular Reactor Nonlinear Models....Pages 159-166 A Feedback Perspective for Chemostat Models with Crowding Effects....Pages 167-174 Positive Control for a Class of Nonlinear Positive Systems....Pages 175-182 Competitive and Cooperative Systems: A Mini-review....Pages 183-190 Small-gain Theorems for Predator-prey Systems....Pages 191-198 Positive Particle Interaction....Pages 199-206 Stability of Linear Systems and Positive Semigroups of Symmetric Matrices....Pages 207-214 Digraph-based Conditioning for Markov Chains....Pages 215-216 Paths and Cycles in the Totally Positive Completion Problem....Pages 217-224 Completion Problems for Positive Matrices with Minimal Rank....Pages 225-232 Some Problems about Structural Properties of Positive Descriptor Systems....Pages 233-240 Positive Linear Systems Reachability Criterion in Digraph Form....Pages 241-248 A Characterization of Reachable Positive Periodic Descriptor Systems....Pages 249-255 A PLDS Model of Pollution in Connected Water Reservoirs....Pages 257-263 Positivity for Matrix Systems: A Case Study from Quantum Mechanics....Pages 265-272 A Simple Food Chain Model with Delay....Pages 273-280 Linear Positive Systems and Phase-type Representations....Pages 281-288 Blending Positive Matrix Pencils with Economic Models....Pages 289-296 On the Positive Reachability of 2D Positive Systems....Pages 297-304 On Nonnegative Realizations....Pages 305-312 Estimation and Strong Approximation of Hidden Markov Models....Pages 313-320 A Paradigm for Derivatives of Positive Systems....Pages 321-328 Nonlinear Positive 2D Systems and Optimal Control....Pages 329-336 State Feedback Set Stabilization for a Class of Nonlinear Systems....Pages 337-344 Some Recent Developments in Positive 2D Systems....Pages 345-352 Nonnegative Infinite Hankel Matrices having a Finite Rank....Pages 353-360 The Character of an Idempotent-analytic Nonlinear Small Gain Theorem....Pages 361-368 Positive Systems with Nondecreasing Controls. Existence and Well-posedness....Pages 369-376 Reachability and Controllability of Positive Linear Discrete-time Systems with Time-delays....Pages 377-384 Countercurrent Double-pipe Heat Exchangers are a Special Type of Positive Systems....Pages 385-392 Note on Structural Properties and Sizes of Eigenspaces of Min-max Functions....Pages 393-400

The proceedings of the First Multidisciplinary International Symposium on Positive Systems Theory and Applications (POSTA 2003) held in Rome, Italy, August 28-30, 2003. Positive Systems are systems in which the relevant variables assume nonnegative values. These systems are quite common in applications where variables represent positive quantities such as populations, goods, money, time, data packets flowing in a network, densities of chemical species, probabilities, etc. The aim of the symposium was to join together researchers working in the different areas related to positive systems such as telecommunications, economy, biomedicine, chemistry and physics in order to provide a multidisciplinary forum where they have the opportunity to exchange ideas and compare results in a unifying framework.

The theory of positive systems can be extended to random positive systems, along lines originally developed by Bellman and extended by Furstenberg and Kesten.