Polynomial and Rational Matrices: Applications in Dynamical Systems Theory

✍ Scribed by Tadeusz Kaczorek (auth.)

• Publisher: Springer-Verlag London
• Year: 2007
• Tongue: English
• Leaves: 513
• Series: Communications and Control Engineering
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Polynomial Matrices....Pages 1-105
Rational Functions and Matrices....Pages 107-162
Normal Matrices and Systems....Pages 163-218
The Problem of Realization....Pages 219-253
Singular and Cyclic Normal Systems....Pages 255-311
Matrix Polynomial Equations, and Rational and Algebraic Matrix Equations....Pages 313-366
The Realisation Problem and Perfect Observers of Singular Systems....Pages 367-419
Positive Linear Systems with Delays....Pages 421-472
Back Matter....Pages 473-503

✦ Subjects

Control Engineering; Systems Theory, Control; Vibration, Dynamical Systems, Control; Circuits and Systems; Linear and Multilinear Algebras, Matrix Theory; Electronic and Computer Engineering