Polynomial and Rational Matrices Applications in Dynamical Systems Theory [Hardcover]

This book reviews new results in the application of polynomial and rational matrices to continuous- and discrete-time systems. It provides the reader with rigorous and in-depth mathematical analysis of the uses of polynomial and rational matrices in the study of dynamical systems. It also throws new light on the problems of positive realization, minimum-energy control, reachability, and asymptotic and robust stability.

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 CayleyHamilton 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.

Polynomial Matrices.- Rational Functions and Matrices.- Normal Matrices and Systems.- The Problem of Realization.- Singular and Cyclic Normal Systems.- Matrix Polynomial Equations, and Rational and Algebraic Matrix Equations.- The Realisation Problem and Perfect Observers of Singular Systems.- Positive Linear Sl£¡