Advances in Time-Delay Systems

1. Front Matter

   Pages I-XIII

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2. Basic Theory

   1. Front Matter

      Pages 1-1

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   2. Basic Theory for Linear Delay Equations

      • Sjoerd M. Verduyn Lunel

      Pages 3-27

3. Stability and Robust Stability

   1. Front Matter

      Pages 29-29

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   2. Complete Type Lyapunov-Krasovskii Functionals

      • Vladimir L. Kharitonov

      Pages 31-42

   3. Robust Stability Conditions of Quasipolynomials by Frequency Sweeping

      • Jie Chen, Silviu-Iulian Niculescu

      Pages 43-60

   4. Improvements on the Cluster Treatment of Characteristic Roots and the Case Studies

      • Rifat Sipahi, Nejat Olgac

      Pages 61-73

   5. From Lyapunov-Krasovskii Functionals for Delay-Independent Stability to LMI Conditions for µ-Analysis

      • Pierre-Alexandre Bliman

      Pages 75-85

4. Control, Identification, and Observer Design

   1. Front Matter

      Pages 87-87

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   2. Finite Eigenstructure Assignment for Input Delay Systems

      • Sabine Mondié, Jean Jacques Loiseau

      Pages 89-101

   3. Control of Systems with Input Delay—An Elementary Approach

      • Vladimir Răsvan, Dan Popescu

      Pages 103-110

   4. On the Stabilization of Systems with Bounded and Delayed Input

      • Frédéric Mazenc, Sabine Mondié, Silviu-Iulian Niculescu

      Pages 111-122

   5. Identifiability and Identification of Linear Systems with Delays

      • Lotfi Belkoura, Michel Dambrine, Yuri Orlov, Jean-Pierre Richard

      Pages 123-135

   6. A Model Matching Solution of Robust Observer Design for Time-Delay Systems

      • Anas Fattouh, Olivier Sename

      Pages 137-152

5. Computation, Software, and Implementation

   1. Front Matter

      Pages 153-153

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   2. Adaptive Integration of Delay Differential Equations

      • Alfredo Bellen, Marino Zennaro

      Pages 155-165

   3. Software for Stability and Bifurcation Analysis of Delay Differential Equations and Applications to Stabilization

      • Dirk Roose, Tatyana Luzyanina, Koen Engelborghs, Wim Michiels

      Pages 167-181

   4. Empirical Methods for Determining the Stability of Certain Linear Delay Systems

      • Richard Datko

      Pages 183-192

   5. Stability Exponent and Eigenvalue Abscissas by Way of the Imaginary Axis Eigenvalues

      • James Louisell

      Pages 193-206

   6. The Effect of Approximating Distributed Delay Control Laws on Stability

      • Wim Michiels, Sabine Mondié, Dirk Roose, Michel Dambrine

      Pages 207-222

In the mathematical description of a physical or biological process, it is a common practice \0 assume that the future behavior of Ihe process considered depends only on the present slate, and therefore can be described by a finite sct of ordinary diffe­ rential equations. This is satisfactory for a large class of practical systems. However. the existence of lime-delay elements, such as material or infonnation transport, of­ tcn renders such description unsatisfactory in accounting for important behaviors of many practical systems. Indeed. due largely to the current lack of effective metho­ dology for analysis and control design for such systems, the lime-delay elements arc often either neglected or poorly approximated, which frequently results in analysis and simulation of insufficient accuracy, which in turns leads to poor performance of the systems designed. Indeed, it has been demonstrated in the area of automatic control that a relatively small delay may lead to instability or significantly deteriora­ ted perfonnances for the corresponding closed-loop systems.

• bifurcation
• communication
• control
• delay
• functional differential equations
• partial differential equation
• robust
• stability

• Centre de Recherche de Royallieu, Universite de Technologie de Compiègne, Compiègne, France

  Silviu-Iulian Niculescu

• Department of Mechanical and Industrial Engineering, Southern Illinois University, Edwardsville, USA

  Keqin Gu

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