# Linear Time-Varying Systems

## Algebraic-Analytic Approach

• Henri Bourlès
• Bogdan Marinescu
Book

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 410)

1. Front Matter
2. ### Mathematical Tools

1. Front Matter
Pages 1-1
2. Henri Bourlès, Bogdan Marinescu
Pages 3-90
3. Henri Bourlès, Bogdan Marinescu
Pages 91-187
4. Henri Bourlès, Bogdan Marinescu
Pages 189-268
5. Henri Bourlès, Bogdan Marinescu
Pages 269-308
3. ### Algebraic Theory of Linear Systems

1. Front Matter
Pages 309-309
2. Henri Bourlès, Bogdan Marinescu
Pages 311-401
3. Henri Bourlès, Bogdan Marinescu
Pages 403-452
4. Henri Bourlès, Bogdan Marinescu
Pages 453-496
4. ### Applications

1. Front Matter
Pages 497-497
2. Henri Bourlès, Bogdan Marinescu
Pages 499-514
3. Henri Bourlès, Bogdan Marinescu
Pages 515-522
4. Henri Bourlès, Bogdan Marinescu
Pages 523-543
5. Henri Bourlès, Bogdan Marinescu
Pages 545-580
5. ### Complements

1. Front Matter
Pages 581-581
2. Henri Bourlès, Bogdan Marinescu
Pages 583-603
6. Back Matter

### Introduction

The aim of this book is to propose a new approach to analysis and control of linear time-varying systems.  These systems are defined in an intrinsic way, i.e., not by a particular representation (e.g., a transfer matrix or a state-space form) but as they are actually.  The system equations, derived, e.g., from the laws of physics, are gathered to form an intrinsic mathematical object, namely a finitely presented module over a ring of operators.  This is strongly connected with the engineering point of view, according to which a system is not a specific set of equations but an object of the material world which can be described by equivalent sets of equations.  This viewpoint makes it possible to formulate and solve efficiently several key problems of the theory of control in the case of linear time-varying systems.  The solutions are based on algebraic analysis.

This book, written for engineers, is also useful for mathematicians since it shows how algebraic analysis can be applied to solve engineering problems.

Henri Bourlès is a Professor and holds the industrial automation chair at the Conservatoire national des arts et métiers in France. He has been teaching automation for over 20 years in engineering and graduate schools.

Bogdan Marinescu is currently research engineer at the French Transmission System Operator (RTE) and Associate Professor at SATIE-Ecole Normale Supérieure de Cachan.

### Keywords

LTV System Linear Time Varying Systems Module Theory Structure at Infinity

#### Authors and affiliations

• Henri Bourlès
• 1
• Bogdan Marinescu
• 2
1. 1.SATIE, CNAM/ENS de CachanCachanFrance
2. 2.RTE EDF TransportVersaillesFrance

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-19727-7
• Copyright Information Springer-Verlag Berlin Heidelberg 2011
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Engineering
• Print ISBN 978-3-642-19726-0
• Online ISBN 978-3-642-19727-7
• Series Print ISSN 0170-8643
• Series Online ISSN 1610-7411
• Buy this book on publisher's site