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Positive linear systems : theory and applications /

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A complete study on an important class of linear dynamical systems-positive linear systemsOne of the most often-encountered systems in nearly all areas of science and technology, positive linear systems is a specific but remarkable and fascinating class. Renowned scientists Lorenzo Farina and Sergio...

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Bibliographic Details
Main Author: Farina, Lorenzo, 1963-
Corporate Author: Wiley InterScience (Online service)
Other Authors: Rinaldi, S. (Sergio), 1940-
Format: eBook
Language:English
Language Notes:English.
Published: New York : Wiley, ©2000.
Series:Pure and applied mathematics (John Wiley & Sons : Unnumbered)
Subjects:
Positive systems.
Non-negative matrices.
Linear systems.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Front Matter
  • Definitions. Introduction
  • 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. Input₆Output Analysis
  • Age-Structured Population Models
  • Markov Chains
  • Compartmental Systems
  • Queueing Systems
  • Conclusions
  • Annotated Bibliography
  • Bibliography
  • Appendix A: Elements of Linear Algebra and Matrix Theory
  • Appendix B: Elements of Linear Systems Theory
  • Index
  • Pure and Applied Mathematics.
  • 2 Definitions and Conditions of Positivity 7
  • 3 Influence Graphs 17
  • 4 Irreducibility, Excitability, and Transparency 23
  • Part II Properties 33
  • 5 Stability 35
  • 6 Spectral Characterization of Irreducible Systems 49
  • 7 Positivity of Equilibria 57
  • 8 Reachability and Observability 65
  • 9 Realization 81
  • 10 Minimum Phase 91
  • 11 Interconnected Systems 101
  • Part III Applications 107
  • 12 Input-Output Analysis 109
  • 13 Age-Structured Population Models 117
  • 14 Markov Chains 131
  • 15 Compartmental Systems 145
  • 16 Queueing Systems 155
  • Appendix A Elements of Linear Algebra and Matrix Theory 187
  • A.1 Real Vectors and Matrices 187
  • A.2 Vector Spaces 189
  • A.3 Dimension of a Vector Space 193
  • A.4 Change of Basis 195
  • A.5 Linear Transformations and Matrices 196
  • A.6 Image and Null Space 198
  • A.7 Invariant Subspaces, Eigenvectors, and Eigenvalues 201
  • A.8 Jordan Canonical Form 207
  • A.9 Annihilating Polynomial and Minimal Polynomial 210
  • A.10 Normed Spaces 212
  • A.11 Scalar Product and Orthogonality 216
  • A.12 Adjoint Transformations 221
  • Appendix B Elements of Linear Systems Theory 225
  • B.1 Definition of Linear Systems 225
  • B.2 ARMA Model and Transfer Function 228
  • B.3 Computation of Transfer Functions and Realization 231
  • B.4 Interconnected Subsystems and Mason's Formula 234
  • B.5 Change of Coordinates and Equivalent Systems 237
  • B.6 Motion, Trajectory, and Equilibrium 238
  • B.7 Lagrange's Formula and Transition Matrix 241
  • B.8 Reversibility 244
  • B.9 Sampled-Data Systems 244
  • B.10 Internal Stability: Definitions 248
  • B.11 Eigenvalues and Stability 248
  • B.12 Tests of Asymptotic Stability 251
  • B.13 Energy and Stability 256
  • B.14 Dominant Eigenvalue and Eigenvector 259
  • B.15 Reachability and Control Law 260
  • B.16 Observability and State Reconstruction 264
  • B.17 Decomposition Theorem 268
  • B.18 Determination of the ARMA Models 272
  • B.19 Poles and Zeros of the Transfer Function 279
  • B.20 Poles and Zeros of Interconnected Systems 282
  • B.21 Impulse Response 286
  • B.22 Frequency Response 288
  • B.23 Fourier Transform 293
  • B.24 Laplace Transform 296
  • B.25 Z-Transform 298
  • B.26 Laplace and Z-Transforms and Transfer Functions 300.