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Input-to-State Stability for PDEs

  • Iasson Karafyllis
  • Miroslav Krstic

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Iasson Karafyllis, Miroslav Krstic
    Pages 1-16
  3. ISS for First-Order Hyperbolic PDEs

    1. Front Matter
      Pages 17-17
    2. Iasson Karafyllis, Miroslav Krstic
      Pages 19-38
    3. Iasson Karafyllis, Miroslav Krstic
      Pages 39-56
  4. ISS for Parabolic PDEs

    1. Front Matter
      Pages 57-59
    2. Iasson Karafyllis, Miroslav Krstic
      Pages 61-92
    3. Iasson Karafyllis, Miroslav Krstic
      Pages 93-140
    4. Iasson Karafyllis, Miroslav Krstic
      Pages 141-182
  5. Small-Gain Analysis

    1. Front Matter
      Pages 183-183
    2. Iasson Karafyllis, Miroslav Krstic
      Pages 185-191
    3. Iasson Karafyllis, Miroslav Krstic
      Pages 193-214
    4. Iasson Karafyllis, Miroslav Krstic
      Pages 215-234
    5. Iasson Karafyllis, Miroslav Krstic
      Pages 235-261
    6. Iasson Karafyllis, Miroslav Krstic
      Pages 263-283
  6. Back Matter
    Pages 285-287

About this book

Introduction

This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools.

In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered:

  • PDEs (of either class) with static maps;
  • PDEs (again, of either class) with ODEs;
  • PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and
  • feedback loops of PDEs of different classes (parabolic with hyperbolic).

In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions.

Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains  a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.

Keywords

Input-to-State Stability Infinite-Dimensional Systems Partial Differential Equations Small-Gain Analysis Stability Theory Disturbance response External stability

Authors and affiliations

  • Iasson Karafyllis
    • 1
  • Miroslav Krstic
    • 2
  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece
  2. 2.Mechanical and Aerospace EngineeringUniversity of CaliforniaSan DiegoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-91011-6
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2019
  • Publisher Name Springer, Cham
  • eBook Packages Intelligent Technologies and Robotics
  • Print ISBN 978-3-319-91010-9
  • Online ISBN 978-3-319-91011-6
  • Series Print ISSN 0178-5354
  • Series Online ISSN 2197-7119
  • Buy this book on publisher's site