Polynomial and Rational Matrices
Applications in Dynamical Systems Theory
Buch in deiner Nähe kaufen
Beschreibung
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.
Matrices are effective tools for modelling and analysing dynamical systems. Professor Kaczorek reviews new results in the application of polynomial and rational matrices to continuous- and discrete-time systems. The book begins with important basics such as the Cayley–Hamilton theorem and elementary operations of polynomial and rational matrices and moves 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 concludes with an appendix describing 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.
Provides the reader with rigorous and in-depth mathematical analysis of the uses of polynomial and rational matrices in the study of dynamical systems Throws new light on the problems of positive realisation, minimum-energy control, reachability, and asymptotic and robust stability Includes supplementary material: sn.pub/extras
Autor*in
Tadeusz Kaczorek
Themen in »Polynomial and Rational Matrices«
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
Stimmen zu »Polynomial and Rational Matrices«
From the reviews:
"It is an excellent book for polynomial and rational matrices and its applications in Dynamical Systems Theory, written by a well-known scientist in the field of control theory. The book can be used either as a reference for researchers in the field of control theory and circuit theory or for teaching for undergraduates or postgraduates in electrical engineering, electronics, mechatronics and computer engineering." (Nicholas Karampetakis, Zentralblatt MATH, Vol. 1114 (16), 2007)
"This book is an extended English version of its original Polish edition based on the author’s lectures to Ph.D. students of electrical engineering. … the book should be useful and accessible to a wide range of researchers and graduate students in applied mathematics, sciences, and engineering because of its thorough and clear presentations of proofs of lemmas and theorems with examples. The application part of the book includes detailed formulation and analysis of problems and step-by-step calculation of solutions to many linear control systems … ." (Miaohua Jiang, SIAM Review, Vol. 51 (3), 2009)
()