Tadeusz Kaczorek Boeken

Focusing on the application of polynomial and rational matrices, the book delves into their role in modeling and analyzing dynamical systems. It starts with foundational concepts like the Cayley-Hamilton theorem and basic matrix operations. Key topics include normal matrices, rational and algebraic polynomial matrix equations, and the development of perfect observers for linear systems. Additionally, it presents new findings on positive linear systems in both discrete and continuous time, particularly those involving delays.

This monograph covers some selected problems of positive fractional 1D and 2D linear systems. It is an extended and modified English version of its preceding Polish edition published by Technical University of Bialystok in 2009. This book is based on the lectures delivered by the author to the Ph. D. students of the Faculty of Electrical Engineering of Bialystok University of Technology and of Warsaw University of Technology and on invited lectures in several foreign universities in the last three years.

This text is devoted to the positive multivariable 1D and 2D linear, time-invariant, finite-dimensional system. The book is based on the author's lectures for Ph.D. students, delivered at Warsaw University of Technology in the academic year 1999/2000. The book consists of two parts; the first part is devoted to the 1D positive linear systems and the second to the 2D positive linear systems described by the Rosser model and the Fornasini-Marchesini models. Definitions, basic properties and theorems concerning positive matrices and graphs are presented; the externally and internally positive linear continuous-time and discrete-time linear systems are considered; and the reachability, controlability and observability of positive linear systems are discussed. The realisation problem for positive 1D and 2D systems is also considered, and the 2D models of externally and internally positive and their properties and controllability and minimum energy control of positive 2D systems are investigated.

W niniejszym podręczniku Autorzy przedstawili podstawy teorii sterowania układów liniowych i nieliniowych, ciągłych i dyskretnych, standardowych i singularnych. Ten praktyczny podręcznik jest przeznaczony dla studentów kierunków technicznych, takich jak elektrotechnika, elektronika i mechatronika, automatyka, robotyka, mechanika oraz informatyka.