Michiels W., Niculescu S.-I. Stability, Control, and Computation for Time-Delay Systems: An Eigenvalue-Based Approach

Philadelphia: SIAM, 2014. — 443 p.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.Preface to the Second Edition
Preface to the First Edition
List of Symbols
AcronymsStability Analysis of Linear Time-Delay SystemsSpectral Properties of Linear Time-Delay Systems
Computation of Characteristic Roots
Pseudospectra and Robust Stability Analysis
Computation of H2 and H-infinity Norms
Computation of Stability Regions in Parameter Spaces
Stability Regions in Delay-Parameter SpacesStabilization and Robust Fixed-Order ControlStabilization Using a Direct Eigenvalue Optimization Approach
Stabilizability with Delayed Feedback: A Numerical Case Study
Optimization of H-infinity NormsApplicationsOutput Feedback Stabilization Using Delays as Control Parameters
Smith predictor for Stable Systems: Delay Sensitivity Analysis
Controlling Unstable Systems Using Finite Spectrum Assignment
Congestion Control Algorithms in Networks
Consensus Problems with Distributed Delays, with Traffic Flow Applications
Synchronization of Delay-Coupled Oscillators
Stability Analysis of Delay Models in BiosciencesAppendix