Stability and Stabilization of Time-Delay Systems. An Eigenvalue-Based Approach
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Author(s): W. Michiels and S.-I. Niculescu
Publisher: SIAM
ISBN: 9780898716320
Format: softback
378pp
Price: $99.00
Review Date: 24 March 2008
Review: When two or more physical systems interconnect there is a transfer such as of material, energy and information. These transports or propagations can be represented by delay elements and the overall system is governed by delay differential equations. These have been well understood particularly from the 1970s, however with the increasing number of applications involving large-scale systems, the delay has become a critical parameter. This has led to the development of numerical algorithms and methods to evaluate such critical delays and the related stability/instability properties, which is the subject of this book. The book also looks at recent approaches in robust control where delays are eventually treated as uncertainty, and the increasing number of efficient algorithms for dealing with nonlinear eigenvalue problems as another important way of dealing with delay systems. The book is in three parts: 1. stability and robust stability which looks at the analysis of linear time-delay systems; 2. Stabilization and robust stabilization looks at synthesis problems of the first part with the focus on stabilization; 3. Applications, which looks at a wide class from congestion analysis in high performance networks, traffic flows and delay models in biosciences. When two or more physical systems interconnect there is a transfer such as of material, energy and information. These transports or propagations can be represented by delay elements and the overall system is governed by delay differential equations. These have been well understood particularly from the 1970s, however with the increasing number of applications involving large-scale systems, the delay has become a critical parameter. This has led to the development of numerical algorithms and methods to evaluate such critical delays and the related stability/instability properties, which is the subject of this book. The book also looks at recent approaches in robust control where delays are eventually treated as uncertainty, and the increasing number of efficient algorithms for dealing with nonlinear eigenvalue problems as another important way of dealing with delay systems. The book is in three parts: 1. stability and robust stability which looks at the analysis of linear time-delay systems; 2. Stabilization and robust stabilization looks at synthesis problems of the first part with the focus on stabilization; 3. Applications, which looks at a wide class from congestion analysis in high performance networks, traffic flows and delay models in biosciences.