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

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  • Formāts: Paperback / softback, 458 pages, height x width x depth: 229x152x20 mm, weight: 830 g, illustrations
  • Sērija : Advances in Design and Control
  • Izdošanas datums: 30-Dec-2014
  • Izdevniecība: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611973627
  • ISBN-13: 9781611973624
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Stability, Control, and Computation for Time-Delay Systems: An Eigenvalue-Based Approach Second EditionPalielināt
  • Formāts: Paperback / softback, 458 pages, height x width x depth: 229x152x20 mm, weight: 830 g, illustrations
  • Sērija : Advances in Design and Control
  • Izdošanas datums: 30-Dec-2014
  • Izdevniecība: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611973627
  • ISBN-13: 9781611973624
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781611973624.html
Keywords:
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 books 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 books 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.
Preface to the Second Edition ix
Preface to the First Edition xv
List of Symbols
xxi
Acronyms xxiii
I Stability analysis of linear time-delay systems
1(190)
1 Spectral properties of linear time-delay systems
3(36)
1.1 Time-delay systems of retarded type
4(10)
1.2 Time-delay systems of neutral type
14(16)
1.3 Systems described by delay-differential algebraic equations
30(6)
1.4 Notes and references
36(3)
2 Computation of characteristic roots
39(30)
2.1 Introduction
39(1)
2.2 Computing all characteristic roots in a right half plane
40(14)
2.3 Neutral systems and delay-differential algebraic equations
54(5)
2.4 Large-scale problems
59(6)
2.5 Notes and references
65(4)
3 Pseudospectra and robust stability analysis
69(24)
3.1 Introduction
69(2)
3.2 Pseudospectra for nonlinear eigenvalue problems
71(7)
3.3 Structured pseudospectra for nonlinear eigenvalue problems
78(6)
3.4 Illustrative examples
84(4)
3.5 Stability radii in delay parameter spaces
88(3)
3.6 Notes and references
91(2)
4 Computation of H2 and H∞ norms
93(26)
4.1 Introduction
93(2)
4.2 Computing H∞ norms
95(15)
4.3 Computing H2 norms
110(7)
4.4 Notes and references
117(2)
5 Computation of stability regions in parameter spaces
119(30)
5.1 Introduction
119(1)
5.2 Basic notions and definitions
120(1)
5.3 From D-decomposition to numerical continuation
121(11)
5.4 Computing the crossing direction of characteristic roots
132(10)
5.5 Computing the root-locus
142(3)
5.6 Notes and references
145(4)
6 Stability regions in delay-parameter spaces
149(42)
6.1 Introduction
149(1)
6.2 Invariance properties
150(3)
6.3 Algebraic methods
153(15)
6.4 Geometric methods
168(12)
6.5 Delay ratio sensitivity and delay-interference phenomenon
180(8)
6.6 Notes and references
188(3)
II Stabilization and robust fixed-order control
191(56)
7 Stabilization using a direct eigenvalue optimization approach
193(18)
7.1 Fixed-order control design
193(1)
7.2 Stabilization via eigenvalue optimization
194(6)
7.3 Numerical examples
200(2)
7.4 Systems described by delay-differential algebraic equations
202(6)
7.5 Notes and references
208(3)
8 Stabilizability with delayed feedback: A numerical case study
211(14)
8.1 Introduction
211(1)
8.2 Characterization of stabilizable systems
212(7)
8.3 Simultaneous stabilization over a delay interval
219(3)
8.4 Stabilizability using Pyragas-type feedback
222(1)
8.5 Notes and references
223(2)
9 Optimization of H∞ norms
225(22)
9.1 Introduction
225(1)
9.2 Motivating examples
226(2)
9.3 Preliminaries
228(2)
9.4 The strong H∞ norm of time-delay systems
230(3)
9.5 Computation of strong H∞ norms
233(5)
9.6 Fixed-order H∞ controller design
238(1)
9.7 Examples
239(4)
9.8 Optimization of stability radii
243(2)
9.9 Notes and references
245(2)
III Applications
247(154)
10 Output feedback stabilization using delays as control parameters
249(36)
10.1 Introduction
249(1)
10.2 Single delay case
250(18)
10.3 Multiple delays case
268(6)
10.4 Network-induced delays case
274(10)
10.5 Notes and references
284(1)
11 Smith predictor for stable systems: Delay sensitivity analysis
285(16)
11.1 Introduction
285(2)
11.2 Sensitivity of stability w.r.t. infinitesimal delay mismatches
287(4)
11.3 Stability analysis and critical delay mismatches
291(2)
11.4 Geometry of stability regions
293(4)
11.5 Multivariable case
297(3)
11.6 Notes and references
300(1)
12 Controlling unstable systems using finite spectrum assignment
301(14)
12.1 Introduction
301(1)
12.2 Preliminaries
302(2)
12.3 Implementation of the integral
304(6)
12.4 Delay mismatch
310(1)
12.5 Output feedback
311(3)
12.6 Notes and references
314(1)
13 Congestion control algorithms in networks
315(22)
13.1 Smith predictor-based congestion control
316(6)
13.2 Algorithms for single connection models with two delays
322(6)
13.3 TCP/AQM congestion avoidance models with one delay
328(6)
13.4 Notes and references
334(3)
14 Consensus problems with distributed delays, with traffic flow applications
337(16)
14.1 Introduction
337(2)
14.2 Extension of stability theory to systems with distributed delays
339(4)
14.3 Conditions for the realization of a consensus
343(5)
14.4 Examples
348(1)
14.5 Other models
349(2)
14.6 Notes and references
351(2)
15 Synchronization of delay-coupled oscillators
353(22)
15.1 Introduction
353(2)
15.2 Preliminaries
355(2)
15.3 Stability analysis of synchronized equilibria
357(4)
15.4 Application to coupled Lorenz systems
361(10)
15.5 Generalizations
371(2)
15.6 Notes and references
373(2)
16 Stability analysis of delay models in biosciences
375(26)
16.1 Introduction
375(1)
16.2 Delay effects on the stability of some biochemical network models
376(5)
16.3 Delay effects on stability in some human respiration models
381(4)
16.4 Delays in immune dynamics models in leukemia
385(14)
16.5 Notes and references
399(2)
Appendix
401(6)
A.1 Rouche's theorem
401(1)
A.2 The structured singular value
401(2)
A.3 Continuity properties
403(1)
A.4 Interdependency of numbers
403(1)
A.5 Software
404(3)
Bibliography 407(26)
Index 433
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 TimeDelay 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-Supélec, 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.