© 2009

Discontinuous Systems

Lyapunov Analysis and Robust Synthesis under Uncertainty Conditions


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

Table of contents

  1. Front Matter
    Pages i-xix
  2. Introduction

    1. Pages 1-10
  3. Mathematical Tools

  4. Synthesis

    1. Front Matter
      Pages 103-104
    2. Pages 105-112
    3. Pages 113-132
  5. Unit Feedback Control of Infinite-dimensional Systems

  6. Electromechanical Applications

  7. Back Matter
    Pages 309-320

About this book


A major problem in control engineering is robust feedback design that stabilizes a nominal plant while also attenuating the influence of parameter variations and external disturbances. This monograph addresses this problem in uncertain discontinuous dynamic systems with special attention to electromechanical systems with hard-to-model nonsmooth phenomena such as friction and backlash. Ignoring these phenomena may severely limit performance so the practical utility of existing smooth control algorithms becomes questionable for many electromechanical applications.

With this motivation, Discontinuous Systems develops nonsmooth stability analysis and discontinuous control synthesis based on novel modeling of discontinuous dynamic systems, operating under uncertain conditions. Although it is primarily a research monograph devoted to the theory of discontinuous dynamic systems, no background in discontinuous systems is required; such systems are introduced in the book at the appropriate conceptual level. Being developed for discontinuous systems, the theory is successfully applied to their subclasses – variable-structure and impulsive systems – as well as to finite- and infinite-dimensional systems such as distributed-parameter and time-delay systems. The presentation concentrates on algorithms rather than on technical implementation although theoretical results are illustrated by electromechanical applications. These specific applications complete the book and, together with the introductory theoretical constituents bring some elements of the tutorial to the text.


Lyapunov Analysis algorithm algorithms calculus control control engineering control theory feedback friction hybrid control modeling robust control stability stabilization uncertainty

Authors and affiliations

  1. 1.Departamento Electrónica y TelecomunicacionesCentro de Investigación Cientifica y Educación Superior de Ensenada (CICESE)EnsenadaMexico

Bibliographic information

Industry Sectors
IT & Software
Energy, Utilities & Environment
Oil, Gas & Geosciences


From the reviews:

“The primary concern of this book is stability analysis and robust control synthesis of uncertain discontinuous systems within the framework of methods of nonsmooth Lyapunov functions. … The book is intended for graduate students and control specialists interested in the discontinuous systems theory and control applications. No background in discontinuous systems is required, as such systems are conceptually introduced at the appropriate level.” (Mircea Crâşmăreanu, Zentralblatt MATH, Vol. 1180, 2010)

“The book is intended for graduate students working in dynamical systems and control as well as industry-based control engineers working in robotics, automotive systems, powertrain control, and aerospace navigation.” (IEEE Control Systems Magazine, Vol. 29, October, 2009)

“This book covers several different topics related to the stability, robust stabilization and control design of discontinuous dynamical systems. … The book is a welcome addition to the literature on discontinuous control systems as the presented results are not readily available in alternative sources. … As a collection of results and applications that are not otherwise readily accessible, the book is a valuable reference for researchers in the field.” (Martin Weiss, Mathematical Reviews, Issue 2012 b)