Time-Delay Systems

Lyapunov Functionals and Matrices

  • Vladimir L. Kharitonov

Part of the Control Engineering book series (CONTRENGIN)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Retarded Type Systems

    1. Front Matter
      Pages 1-1
    2. Vladimir L. Kharitonov
      Pages 3-26
    3. Vladimir L. Kharitonov
      Pages 27-74
    4. Vladimir L. Kharitonov
      Pages 75-131
    5. Vladimir L. Kharitonov
      Pages 133-170
  3. Neutral Type Systems

    1. Front Matter
      Pages 171-171
    2. Vladimir L. Kharitonov
      Pages 173-200
    3. Vladimir L. Kharitonov
      Pages 201-254
    4. Vladimir L. Kharitonov
      Pages 255-304
  4. Back Matter
    Pages 305-311

About this book


Stability is one of the most studied issues in the theory of time-delay systems, but the corresponding chapters of published volumes on time-delay systems do not include a comprehensive study of a counterpart of classical Lyapunov theory for linear delay free systems. The principal goal of the book is to fill this gap, and to provide readers with a systematic and exhaustive treatment of the basic concepts of the Lyapunov-Krasovskii approach to the stability analysis of linear time-delay systems.​

The book is organized into two parts. The first part is dedicated to the case of retarded type time-delay systems; it consists of four chapters, which respectively deal with results concerning the existence and uniqueness of the solutions of an initial value problem, the class of linear systems with one delay, the case of systems with several delays, and the case of systems with distributed delays. The second part of the book studies the case of neutral type time-delay systems, containing three chapters that extend the results presented earlier in the book to neutral time-delay systems and treating special classes of linear time-delay systems. 

Time-Delay Systems: Lyapunov Functionals and Matrices will be of great use and interest to researchers and graduate students in automatic control and applied mathematics as well as practicing engineers involved in control system design.​


Lyapunov functionals Lyapunov matrices Lyapunov-Krasovskii approach complete type functional exponential stability time-delay systems

Authors and affiliations

  • Vladimir L. Kharitonov
    • 1
  1. 1., Faculty of Applied MathematicsSaint Petersburg State UniversitySaint PetersburgRussia

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