Stability, Control, and Computation for Time-Delay Systems: An Eigenvalue-Based Approach, Second Edition

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; and increase the number and range of applications to better illustrate the effectiveness and generality of their approach.

Audience: Engineers, researchers, and graduate students in control and systems engineering, as well as computational and applied mathematicians, will find this book of great interest. It will also be of value to undergraduate and graduate students and laboratory researchers.

Contents: Preface to the Second Edition; Preface to the First Edition; List of Symbols: Acronyms; 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; Appendix; Bibliography; Index