# Multivariable Computer-controlled Systems

## A Transfer Function Approach

• Efim N. Rosenwasser
• Bernhard P. Lampe
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

• Efim N. Rosenwasser
• 1
• Bernhard P. Lampe
• 2
1. 1.State Marine Technical UniversitySaint PetersburgRussia
2. 2.Institute of AutomationUniversity of RostockRostockGermany

### Bibliographic information

• DOI https://doi.org/10.1007/1-84628-432-5
• Copyright Information Springer-Verlag London Limited 2006
• Publisher Name Springer, London
• eBook Packages Engineering
• Print ISBN 978-1-84628-431-1
• Online ISBN 978-1-84628-432-8
• Series Print ISSN 0178-5354
• Buy this book on publisher's site
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