# Multivariable Computer-controlled Systems

## A Transfer Function Approach

Book

Part of the Communications and Control Engineering book series (CCE)

1. Front Matter
Pages i-xvii
2. ### Algebraic Preliminaries

1. Front Matter
Pages 1-1
2. Pages 3-51
3. Pages 53-104
4. Pages 105-145
3. ### General MIMO Control Problems

1. Front Matter
Pages 147-147
4. ### Frequency Methods for MIMO SD Systems

1. Front Matter
Pages 239-239
5. Back Matter
Pages 429-478

### Introduction

The transfer function approach is widely used in classical control theory for its easy handling and physical meaning. Although the use of transfer functions is well-established for linear time-invariant systems, it is not suitable for non-stationary systems among which are sampled-data systems and processes with periodically varying coefficients. Computer-controlled continuous-time processes are a very important subset of periodic sampled-data systems which are not treatable using ordinary transfer functions.

Having established the ability of the parametric transfer function to solve this problem for single-input, single-output systems in previous work, the authors extend these methods, which incorporate time-dependence, to the idea of the parametric transfer matrix in a complete exposition of analysis and design methods for multiple-input, multiple-output (MIMO) sampled-data systems.

Multivariable Computer-controlled Systems is divided into three parts:

• Preliminary algebraic material describing the established fundamentals of polynomial and rational matrices necessary for the understanding of later chapters.

• Control problems, important in their own right but which also have a substantial bearing on what follows (eigenvalue assignment and the use of z- and zeta-transforms in discrete systems).

• Frequency methods for the investigation of MIMO sampled-data systems (parametric discrete-time models; stability; stochastic methods; H2 optimization and L2 design).

Appendices covering basic mathematical formulae and the description of two MATLAB® toolboxes round out this self-contained guide to multivariable control systems.

Of special interest to researchers in automatic control and to development engineers working with advanced control technology, Multivariable Computer-controlled Systems will also interest mathematical control theorists and graduate students studying advanced methods of computer-based control.

### Keywords

MIMO Norm Normal Stabilisation Standard development optimization technology

#### Authors and affiliations

1. 1.State Marine Technical UniversitySaint PetersburgRussia
2. 2.Institute of AutomationUniversity of RostockRostockGermany

#### About the authors

E.N. Rosenwasser holds the chair for automated ship complexes at the State University of Ocean Technology of Saint Petersburg, Russia. Prof. Rosenwasser is one of the leading Russian control scientists. His research results are published in more than 200 publications including 15 monographs.

Bernhard P. Lampe is Professor for automatic control at the Institute of Automation, Department Electrical Engineering and Computer Sciences at the University of Rostock, Germany. Prof. Lampe is initiator and leader of numerous research projects in theory and application of advanced control methods, as well as author and co-author of more than 250 publications including 5 monographs.

In cooperation both authors wrote the Communications and Control Engineering monograph Computer Controlled Systems, (1-85233-307-3, 2000).

### Bibliographic information

• Book Title Multivariable Computer-controlled Systems
• Book Subtitle A Transfer Function Approach
• Authors Efim N. Rosenwasser
Bernhard P. Lampe
• Series Title Communications and Control Engineering
• DOI https://doi.org/10.1007/1-84628-432-5
• Copyright Information Springer-Verlag London Limited 2006
• Publisher Name Springer, London
• eBook Packages Engineering Engineering (R0)
• Hardcover ISBN 978-1-84628-431-1
• Softcover ISBN 978-1-84996-600-9
• eBook ISBN 978-1-84628-432-8
• Series ISSN 0178-5354
• Edition Number 1
• Number of Pages XVIII, 478
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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## Reviews

From the reviews:

"The monograph throws the bridge between continuous and discrete control systems. … The authors extend known approaches to achieve a comprehensive analysis of computer control systems belonging to the class of sampled data systems. … The book contains also an Appendix providing additional mathematical problems, description of the toolbox for optimal design multivariable sampled data systems and design towards achieving a guaranteed control system performance. The book is very interesting for researchers and graduate students who want to extend their knowledge on modern control systems." (Krzysztof Galkowski, Zentralblatt MATH, Vol. 1123 (1), 2008)

“Multivariable Computer-Controlled Systems is dedicated to the theory of multivariable control systems, and the material is presented in a formal, mathematical style. … The book also contains several appendices, including a description of a Matlab toolbox for controller design. … the authors have done an admirable job in collecting the necessary material in one place … . experts will no doubt value the book for its concise presentation and its focused approach … .” (Matthew C. Turner, IEEE Control Systems Magazine, Vol. 28, December, 2008)