Robust Nonlinear Control Design

State-Space and Lyapunov Techniques

  • Randy A. Freeman
  • Petar Kokotović

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Randy A. Freeman, Petar Kokotović
    Pages 1-13
  3. Randy A. Freeman, Petar Kokotović
    Pages 15-32
  4. Randy A. Freeman, Petar Kokotović
    Pages 33-63
  5. Randy A. Freeman, Petar Kokotović
    Pages 65-100
  6. Randy A. Freeman, Petar Kokotović
    Pages 101-136
  7. Randy A. Freeman, Petar Kokotović
    Pages 137-160
  8. Randy A. Freeman, Petar Kokotović
    Pages 161-202
  9. Randy A. Freeman, Petar Kokotović
    Pages 203-228
  10. Back Matter
    Pages 229-257

About this book


This book presents advances in the theory and design of robust nonlinear control systems. In the first part of the book, the authors provide a unified framework for state-space and Lyapunov techniques by combining concepts from set-valued analysis, Lyapunov stability theory, and game theory. Within this unified framework, the authors then develop a variety of control design methods suitable for systems described by low-order nonlinear ordinary differential equations. Emphasis is placed on global controller designs, that is, designs for the entire region of model validity. Because linear theory deals well with local system behavior (except for critical cases in which Jacobian linearization fails), the authors focus on achieving robustness and performance for large deviations from a given operation condition.

The purpose of the book is to summarize Lyapunov design techniques for nonlinear systems and to raise important issues concerning large-signal robustness and performance. The authors have been the first to address some of these issues, and they report their findings in this text. For example, they identify two potential sources of excessive control effort in Lyapunov design techniques and show how such effort can be greatly reduced.

The researcher who wishes to enter the field of robust nonlinear control could use this book as a source of new research topics. For those already active in the field, the book may serve as a reference to a recent body of significant work. Finally, the design engineer faced with a nonlinear control problem will benefit from the techniques presented here.


"The text is practically self-contained. The authors offer all necessary definitions and give a comprehensive introduction. Only the most basic knowledge of nonlinear analysis and design tools is required, including Lyapunov stability theory and optimal control. The authors also provide a review of set-valued maps for those readers who are not familiar with set-valued analysis. The book is intended for graduate students and researchers in control theory, serving as both a summary of recent results and a source of new research problems. In the opinion of this reviewer the authors do succeed in attaining these objectives."   — Mathematical Reviews



Lyapunov stability game theory mathematics nonlinear ordinary differential equations nonlinear systems robust nonlinear control set-valued analysis state-space techniques systems and control control control system control theory design differential equation model nonlinear control nonlinear system Optimal control ordinary differential equation signal stability stability theory

Authors and affiliations

  • Randy A. Freeman
    • 1
  • Petar Kokotović
    • 2
  1. 1.Department of Electrical and Computer EngineeringNorthwestern UniversityEvanstonUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of CaliforniaSanta BarbaraUSA

Bibliographic information