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Positive 1D and 2D Systems

In the last decade a dynamic development in positive systems has been observed. Roughly speaking, positive systems are systems whose inputs, state variables and outputs take only nonnegative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers an...

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Bibliographic Details
Main Author: Kaczorek, Tadeusz
Format: eBook
Language:English
Published: London Springer London 2002, 2002
Edition:1st ed. 2002
Series:Communications and Control Engineering
Subjects:
Computer Communication Networks
Control And Systems Theory
Control Theory
Systems Theory, Control
Computer Networks 
System Theory
Control Engineering
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 4.3 Existence and computation of positive realisations of multi-input multi-output systems
  • 4.4 Existence and computation of positive realisations of weakly positive multi-input multi-output systems
  • 4.5 Positive realisations in canonical forms of singular linear
  • Problems
  • References
  • 5. 2D models of positive linear systems
  • 5.1 Internally positive Roesser model
  • 5.2 Externally positive Roesser model
  • 5.3 Internally positive general model
  • 5.4 Externally positive general model
  • 5.5 Positive Fornasini-Marchesini models and relationships between models
  • 5.6 Positive models of continuous-discrete systems
  • 5.7 Positive generalised Roesser model
  • Problems
  • References
  • 6 Controllability and minimum energy control of positive 2D systems
  • 6.1 Reachability, controllability and observability of positive Roesser model
  • 6.2 Reachability, controllability and observability of the positive general model
  • 6.3 Minimum energy control of positive 2D systems
  • 1. Positive matrices and graphs
  • 1.1 Generalised permutation matrix, nonnegative matrix, positive and strictly positive matrices
  • 1.2 Reducible and irreducible matrices
  • 1.3 The Collatz — Wielandt function
  • 1.4 Maximum eigenvalue of a nonnegative matrix
  • 1.5 Bounds on the maximal eigenvalue and eigenvector of a positive matrix
  • 1.6 Dominating positive matrices of complex matrices
  • 1.7 Oscillatory and primitive matrices
  • 1.8 The canonical Frobenius form of a cyclic matrix
  • 1.9 Metzler matrix
  • 1.10 M-matrices
  • 1.11 Totally nonnegative (positive) matrices
  • 1.12 Graphs of positive systems
  • 1.13 Graphs of reducible, irreducible, cyclic and primitive systems
  • Problems
  • References
  • 2. Continuous-ime and discrete-ime positive systems
  • 2.1 Externally positive systems
  • 2.2 Internally positive systemst
  • 2.3 Compartmental systems
  • 2.4 Stability of positive systems
  • 2.5 Input-output stability
  • 2.6 Weakly positive systems
  • 2.7 Componentwise asymptotic stability and exponental stability of positive systems
  • 2.8 Externally and internally positive singular systems
  • 2.9 Composite positive linear systems
  • 2.10 Eigenvalue assignment problem for positive linear systems
  • Problems
  • References
  • 3. Reachability, controllability and observability of positive systems
  • 3.1 discrete-time systems
  • 3.2 continuous-time systems
  • 3.3 Controllability of positive systems
  • 3.4 Minimum energy control of positive systems
  • 3.5 Reachability and controllability of weakly positive systems with state feedbacks
  • 3.6 Observability of discrete-time positive systems
  • 3.7 Reachability and controllability of weakly positive systems
  • Problems
  • References
  • 4. Realisation problem of positive 1D systems
  • 4.1 Basic notions and formulation of realisation problem
  • 4.2 Existence andcomputation of positive realisations
  • 6.4 Reachability and minimum energy control of positive 2D continuous-discrete systems
  • Problems
  • References
  • 7. Realisation problem for positive 2D systems
  • 7.1 Formulation of realisation problem for positive Roesser model
  • 7.2 Existence of positive realisations
  • 7.3 Positive realisations in canonical form of the Roesser model
  • 7.4 Determination of the positive Roesser model by the use of state variables diagram
  • 7.5 Determination of a positive 2D general model for a given transfer matrix
  • 7.6 Positive realisation problem for singular 2D Roesser model
  • 7.7 Concluding remarks and open problems
  • Problems
  • References
  • Appendix A Oeterminantal Sylvester equality
  • Appendix B Computation of fundamental matrices of linear systems
  • Appendix C Solutions of 20 linear discrete models
  • Appendix D Transformations of matrices to their canonical forms and lemmas for 1D singular systems

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