Time delays are important components of many systems in, for instance, engineering, physics, economics, and the life sciences, because the transfer of material, energy, and information is usually not instantaneous. Time delays may appear as computation and communication lags, they model transport phenomena and heredity, and they arise as feedback delays in control loops. This monograph addresses the problem of stability analysis, stabilization, and robust fixed-order control of dynamical systems subject to delays, including both retarded- and neutral-type systems. Within the eigenvalue-based framework, an overall solution is given to the stability analysis, stabilization, and robust control design problem, using both analytical methods and numerical algorithms and applicable to a broad class of linear time-delay systems. In this revised edition, the authors: Make the leap from stabilization to the design of robust and optimal controllers and from retarded-type to neutral-type delay systems, thus enlarging the scope of the book within control. Include new, state-of-the-art material on numerical methods and algorithms to broaden the book's focus and to reach additional research communities, in particular numerical linear algebra and numerical optimization. Increase the number and range of applications to better illustrate the effectiveness and generality of their approach. In this revised edition, the authors make the leap from stabilization to the design of robust and optimal controllers and from retarded-type to neutral-type delay systems, thus enlarging the scope of the book within control; include new, state-of-the-art material on numerical methods and algorithms to broaden the book's focus and to reach additional research communities, in particular numerical linear algebra and numerical optimization; and increase the number and range of applications to better illustrate the effectiveness and generality of their approach.
Wim Michiels is an associate professor at KU Leuven, where he leads a research team within the Numerical Analysis and Applied Mathematics Division. He has coauthored more than 75 journal papers in the areas of control and optimization and computational and applied mathematics, coauthored the monograph Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach (SIAM, 2007), and coedited three other books. Silviu-Iulian Niculescu is senior researcher at CNRS at the Laboratory of Signals and Systems (L2S), CNRS-Supelec, Gif-sur-Yvette, France. In 2006 he joined the L2S, which he has headed since January 2010. He is the coauthor of more than 400 book chapters, journal papers, and communications in international conferences, has coauthored five books, and is coeditor of six multiauthor volumes.
Part I: Stability Analysis of Linear Time-Delay Systems Chapter 1: Spectral Properties of Linear Time-Delay Systems Chapter 2: Computation of Characteristic Roots Chapter 3: Pseudospectra and Robust Stability Analysis Chapter 4: Computation of H2 and H-infinity Norms Chapter 5: Computation of Stability Regions in Parameter Spaces Chapter 6: Stability Regions in Delay-Parameter Spaces Part II: Stabilization and Robust Fixed-Order Control Chapter 7: Stabilization Using a Direct Eigenvalue Optimization Approach Chapter 8: Stabilizability with Delayed Feedback: A Numerical Case Study Chapter 9: Optimization of H-infinity Norms Part III: Applications Chapter 10: Output Feedback Stabilization Using Delays as Control Parameters Chapter 11: Smith predictor for Stable Systems: Delay Sensitivity Analysis Chapter 12: Controlling Unstable Systems Using Finite Spectrum Assignment Chapter 13: Congestion Control Algorithms in Networks Chapter 14: Consensus Problems with Distributed Delays, with Traffic Flow Applications Chapter 15: Synchronization of Delay-Coupled Oscillators Chapter 16: Stability Analysis of Delay Models in Biosciences
