© 2007

Algebraic Methods for Nonlinear Control Systems


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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Methodology

    1. Front Matter
      Pages 1-1
    2. Pages 3-19
    3. Pages 21-43
    4. Pages 45-54
    5. Pages 55-69
    6. Pages 89-102
  3. Applications to Control Problems

    1. Front Matter
      Pages 103-103
    2. Pages 115-118
    3. Pages 127-129
    4. Pages 131-148
  4. Back Matter
    Pages 167-178

About this book


A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students.

The most popular treatment of control for nonlinear systems is from the viewpoint of differential geometry yet this approach proves not to be the most natural when considering problems like dynamic feedback and realization. Professors Conte, Moog and Perdon develop an alternative linear-algebraic strategy based on the use of vector spaces over suitable fields of nonlinear functions. This algebraic perspective is complementary to, and parallel in concept with, its more celebrated differential-geometric counterpart.

Algebraic Methods for Nonlinear Control Systems describes a wide range of results, some of which can be derived using differential geometry but many of which cannot. They include:

• classical and generalized realization in the nonlinear context;

• accessibility and observability recast within the linear-algebraic setting;

• discussion and solution of basic feedback problems like input-to-output linearization, input-to-state linearization, non-interacting control and disturbance decoupling;

• results for dynamic and static state and output feedback.

Dynamic feedback and realization are shown to be dealt with and solved much more easily within the algebraic framework.

Originally published as Nonlinear Control Systems, 1-85233-151-8, this second edition has been completely revised with new text – chapters on modeling and systems structure are expanded and that on output feedback added de novo – examples and exercises. The book is divided into two parts: the first being devoted to the necessary methodology and the second to an exposition of applications to control problems.


Control Control Theory Dynamic State Feedback Linear Algebra Nonlinear Control Nonlinear Systems Systems Theory modeling nonlinear control system nonlinear system

Authors and affiliations

  1. 1.Dipartimento di Ingegneria Informatica Gestionale e dell’AutomazioneUniversità Politecnica delle MarcheAnconaItaly
  2. 2.Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN)Centre National de la Recherche Scientifique (CNRS)Nantes Cedex 3France

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From the reviews of the second edition: “Algebraic Methods for Nonlinear Control Systems is a book published under the Springer Communication and Control Engineering publication program, which presents major technological advances within these fields. The book aims at presenting one of the two approaches to nonlinear control systems, namely the differential algebraic method. … is an excellent textbook for graduate courses on nonlinear control systems. … The differential algebraic method presented in this book appears to be an excellent tool for solving the problems associated with nonlinear systems.” (Dariusz Bismor, International Journal of Acoustics and Vibration, Vol. 14 (4), 2009)