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Positive 1D and 2D Systems

  • Book
  • © 2002

Overview

Authors:
  1. Tadeusz Kaczorek

    1. Institute of Control and Industrial Electronics, Faculty of Electrical Engineering, Warsaw University of Technology, Warsaw, Poland

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  • Will give the reader tools for dealing with uncertainty in control systems which are more advanced and flexible than either traditional optimal control or robust control.
  • Reduces the computational cost of high-quality control and the complexity of the algorithms involved making similar results achievable with less effort by the user.

Part of the book series: Communications and Control Engineering (CCE)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Positive matrices and graphs

    • Tadeusz Kaczorek
    Pages 1-49

  3. Continuous-time and discrete-time positive systems

    • Tadeusz Kaczorek
    Pages 51-126

  4. Reachability, controllability and observability of positive systems

    • Tadeusz Kaczorek
    Pages 127-172

  5. Realisation problem of positive 1D systems

    • Tadeusz Kaczorek
    Pages 173-240

  6. 2D models of positive linear systems

    • Tadeusz Kaczorek
    Pages 241-273

  7. Controllability and minimum energy control of positive 2D systems

    • Tadeusz Kaczorek
    Pages 275-309

  8. Realisation problem for positive 2D systems

    • Tadeusz Kaczorek
    Pages 311-366

  9. Back Matter

    Pages 367-431
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Keywords

About this book

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 and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear system behaviour can be found in engineering, management science, economics, social sciences, biology and medicine, etc. The basic mathematical tools for analysis and synthesis of linear systems are linear spaces and the theory of linear operators. Positive linear systems are defined on cones and not on linear spaces. This is why the theory of positive systems is more complicated and less advanced. The theory of positive systems has some elements in common with theories of linear and non-linear systems. Schematically the relationship between the theories of linear, non-linear and positive systems is shown in the following figure Figure 1.

Authors and Affiliations

  • Institute of Control and Industrial Electronics, Faculty of Electrical Engineering, Warsaw University of Technology, Warsaw, Poland

    Tadeusz Kaczorek

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