Advanced H∞ Control

Towards Nonsmooth Theory and Applications

  • Yury V. Orlov
  • Luis T. Aguilar

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Introduction

    1. Front Matter
      Pages 1-4
    2. Yury V. Orlov, Luis T. Aguilar
      Pages 5-21
    3. Yury V. Orlov, Luis T. Aguilar
      Pages 23-41
    4. Yury V. Orlov, Luis T. Aguilar
      Pages 43-53
    5. Yury V. Orlov, Luis T. Aguilar
      Pages 55-63
  3. Nonsmooth $$\mathcal{H}_{\infty }$$ Control

    1. Front Matter
      Pages 65-66
    2. Yury V. Orlov, Luis T. Aguilar
      Pages 67-80
    3. Yury V. Orlov, Luis T. Aguilar
      Pages 81-104
  4. Benchmark Applications

  5. Back Matter
    Pages 211-218

About this book


This compact monograph is focused on disturbance attenuation in nonsmooth dynamic systems, developing an H approach in the nonsmooth setting. Similar to the standard nonlinear Happroach, the proposed nonsmooth design guarantees both the internal asymptotic stability of a nominal closed-loop system and the dissipativity inequality, which states that the size of an error signal is uniformly bounded with respect to the worst-case size of an external disturbance signal. This guarantee is achieved by constructing an energy or storage function that satisfies the dissipativity inequality and is then utilized as a Lyapunov function to ensure the internal stability requirements. 


Advanced H Control is unique in the literature for its treatment of disturbance attenuation in nonsmooth systems. It synthesizes various tools, including Hamilton–Jacobi–Isaacs partial differential inequalities​ as well as Linear Matrix Inequalities. Along with the finite-dimensional treatment, the synthesis is extended to infinite-dimensional setting, involving time-delay and distributed parameter systems. To help illustrate this synthesis, the book focuses on electromechanical applications with nonsmooth phenomena caused by dry friction, backlash, and sampled-data measurements. Special attention is devoted to implementation issues. 


Requiring familiarity with nonlinear systems theory, this book wi

ll be accessible to graduate students interested in systems analysis and design, and is a welcome addition to the literature for researchers and practitioners in these areas.


H-infinity Lyapunov function backstepping approach disturbance attenuation nonsmooth analysis and systems robust, H-infinity, and sliding mode control underactuated system

Authors and affiliations

  • Yury V. Orlov
    • 1
  • Luis T. Aguilar
    • 2
  1. 1.Electronics and Telecommunications Dept.CICESE Research CenterEnsenadaMexico
  2. 2.Centro de Investigación y Desarrollo de Tecnología DigitalInstituto Politécnico NacionalTijuanaMexico

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-0291-0
  • Online ISBN 978-1-4939-0292-7
  • Series Print ISSN 2324-9749
  • Series Online ISSN 2324-9757
  • Buy this book on publisher's site