First-order Representations of Linear Systems

• Margreet Kuijper
Book

Part of the Systems & Control: Foundations & Applications book series (SCFA)

1. Front Matter
Pages i-viii
2. Margreet Kuijper
Pages 3-13
3. Margreet Kuijper
Pages 14-39
4. Margreet Kuijper
Pages 40-70
5. Margreet Kuijper
Pages 71-105
6. Margreet Kuijper
Pages 106-143
7. Margreet Kuijper
Pages 144-185
8. Margreet Kuijper
Pages 186-187
9. Back Matter
Pages 188-198

Introduction

This book is about the theory of system representations. The systems that are considered are linear, time-invariant, deterministic and finite­ dimensional. The observation that some representations are more suitable for handling a particular problem than others motivates the study of rep­ resentations. In modeling a system, a representation often arises naturally from certain laws that underlie the system. In its most general form the representation then consists of dynamical equations for the system compo­ nents and of constraint equations reflecting the connection between these components. Depending on the particular problem that is to be inves­ tigated, it will sometimes be useful to rewrite the equations, that is, to transform the representation. For this reason it is of special importance to derive transformations that enable one to switch from one representation to another. A new approach of the past decade has been the so-called "behavioral ap­ proach" introduced by Willems. One of the main features of the behavioral approach is that it is well suited for modeling the interconnection of sys­ tems. It is for this reason that the behavioral approach is a natural choice in the context of modeling. In this book we adopt the behavioral approach: we define a system as a "behavior" , that is, a set of trajectories whose math­ ematical representation by means of differential or difference equations is nonunique. An aspect of this approach that is important in the context of representation theory is the fact that a natural type of equivalence arises.

Keywords

Finite Invariant equation linear systems modeling representations system transformation

Authors and affiliations

• Margreet Kuijper
• 1
1. 1.Department of MathematicsUniversity of GröningenGröningenThe Netherlands

Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-0259-2
• Copyright Information Birkhäuser Boston 1994
• Publisher Name Birkhäuser, Boston, MA
• eBook Packages
• Print ISBN 978-1-4612-6684-6
• Online ISBN 978-1-4612-0259-2
• Series Print ISSN 2324-9749
• Buy this book on publisher's site