Analysis of Positive Descriptor Systems : Topics in Systems and Control Theory

Elena Virnik

ISBN 10: 363906058X / ISBN 13: 9783639060584

Published by VDM Verlag Dr. Müller, VDM Verlag Dr. Müller E.K., 2008

About this Item

Neuware - Positive systems arise naturally in many areas of biology or medicine, where the variables represent nonnegative quantities such as concentrations or population numbers of bacteria or cells. One encounters such systems also in economy, where the aim is to predict prices or productions.With this work we aim to lay the theoretical foundation for understanding positive descriptor systems in the continuous-time and in the discrete-time case. We present a cohesive framework that allows to generalise many results for standard positive systems to the descriptor case.We define and characterise positive descriptor systems and analyse their properties. We establish two fundamental results, pertinent to the area of nonnegative matrix theory, that play a crucial role in the analysis of such systems. Furthermore, we treat central topics from systems and control theory, such as stability properties, existence of doubly nonnegative solutions of generalised Lyapunov equations and positivity preserving model reduction. The present work is directed at students or professionals seeking an introduction into the field of positive descriptor systems or aiming to conduct further research in this area.

Seller Inventory # 9783639060584

Bibliographic Details

• Title: Analysis of Positive Descriptor Systems : Topics in Systems and Control Theory
• Publisher: VDM Verlag Dr. Müller, VDM Verlag Dr. Müller E.K.
• Publication Date: 2008
• Language: English
• ISBN 10: 363906058X
• ISBN 13: 9783639060584
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 9D millimeters 220 millimeters width by 150 millimeters height by 9 millimeters depth
• Weight: 244 grams

About this title

Synopsis

Positive systems arise naturally in many areas of biology or medicine, where the variables represent nonnegative quantities such as concentrations or population numbers of bacteria or cells. One encounters such systems also in economy, where the aim is to predict prices or productions. With this work we aim to lay the theoretical foundation for understanding positive descriptor systems in the continuous-time and in the discrete-time case. We present a cohesive framework that allows to generalise many results for standard positive systems to the descriptor case. We define and characterise positive descriptor systems and analyse their properties. We establish two fundamental results, pertinent to the area of nonnegative matrix theory, that play a crucial role in the analysis of such systems. Furthermore, we treat central topics from systems and control theory, such as stability properties, existence of doubly nonnegative solutions of generalised Lyapunov equations and positivity preserving model reduction. The present work is directed at students or professionals seeking an introduction into the field of positive descriptor systems or aiming to conduct further research in this area.

About the Author

Dr. Elena Virnik: Research assistant at the DFG Research Center MATHEON in Berlin, application area: life sciences. PhD in mathematics at TU Berlin, 2008. Diploma in mathematics with finance at TU Berlin and London City University, 2005.