Polynomial and Rational Matrices

Applications in Dynamical Systems Theory

  • Tadeusz Kaczorek

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

About this book


Matrices are effective tools for the modelling and analysis of dynamical systems. Professor Kaczorek gives an overview of new results in the application of polynomial and rational matrices to continuous- and discrete-time systems. The book is self-contained, beginning with important basics such as the Cayley–Hamilton theorem and definitions and elementary operations of polynomial and rational matrices and moving on to cover such topics as:

• normal matrices (including their realisation);

• rational and algebraic polynomial matrix equations;

• perfect observers for and realisation of linear systems; and

• new results on positive linear discrete- and continuous-time systems with delays.

The text is rounded off with an appendix describing fundamental definitions and theorems relevant to controllability and observability in linear systems.

Polynomial and Rational Matrices will be valuable to researchers in control and/or system theory and will provide useful reference material for graduates studying courses in electronic and computer engineering, mechatronics and electrical engineering.


Control Theory Discrete-time Systems Dynamical Systems Linear Systems Matrix Normal Matrices Polynomial Matrices Rational Functions Rational Matrices dynamische Systeme electrical engineering mechatronics modeling stability systems theory

Authors and affiliations

  • Tadeusz Kaczorek
    • 1
  1. 1.Institute of Control and Industrial Electronics, Faculty of Electrical EngineeringWarsaw University of TechnologyWarsawPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84628-605-6
  • Copyright Information Springer-Verlag London Limited 2007
  • Publisher Name Springer, London
  • eBook Packages Engineering
  • Print ISBN 978-1-84628-604-9
  • Online ISBN 978-1-84628-605-6
  • Series Print ISSN 0178-5354
  • About this book