Topics in Multidimensional Linear Systems Theory

✍ Scribed by Eva Zerz

• Publisher: Springer
• Year: 2000
• Tongue: English
• Leaves: 175
• Series: Lecture Notes in Control and Information Sciences
• Edition: 1st Edition.
• Category: Library

✦ Synopsis

The past few decades have witnessed an increasing interest in the field of multidimensional systems theory. This is concerned with systems whose trajectories depend not on one single variable (usually interpreted as time or frequency), but on several independent variables, such as the coordinates of an image.The behavioural approach introduced by J. C. Willems provides a particularly suitable framework for developing a linear systems theory in several variables. The book deals with the classical concepts of autonomy, controllability, observability, and stabilizability. All the tests and criteria given are constructive in the sense that algorithmic versions may be implemented in modern computer algebra systems, using Gr?bner basis techniques.There is a close connection between multidimensional systems theory and robust control of one-dimensional systems with several uncertain parameters. The central link consists in the basic tool of linear fractional transformations. The book concludes with examples from the theory of electrical networks.

✦ Table of Contents

Lecture Notes in Control and Information Sciences 256......Page 2
Preface......Page 6
Organization and Summary......Page 7
Table of Contents......Page 9
1. Controllability of Multidimensional Systems......Page 11
2. Co-prime Factorizations of Multivariate Rational Matrices......Page 51
3. Stabilizability......Page 67
4. Strict System Equivalence......Page 78
5. First Order Representations o fMultidimensional Systems......Page 94
6. Linear Fractional Transformations......Page 114
7 . Electrical Networks......Page 150
List of Acronyms......Page 166
Index......Page 172
Lecture Notes in Control and Information Sciences......Page 174