Discontinuous Systems

Lyapunov Analysis and Robust Synthesis under Uncertainty Conditions

  • Yury V. Orlov

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

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

Bibliographic information