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.
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.
This book develops original results regarding singular dynamic systems following two different paths. The first consists of generalizing results from classical state-space cases to linear descriptor...
This book covers some selected problems of the descriptor integer and fractional order positive continuous-time and discrete-time systems.The book consists of 3 chapters, 4 appendices and the list of...
This thesis develops several systematic and unified approaches for analyzing dynamic systems with positive characteristics or a more general cone invariance property. Based on these analysis...
This thesis introduces novel and significant results regarding the analysis and synthesis of positive systems, especially under l1 and L1 performance. It describes stability analysis, controller...
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