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Absolute Stability of Nonlinear Control Systems

  • Xiaoxin Liao

Part of the Mathematics and Its Applications (Chinese Series) book series (MACA, volume 5)

Table of contents

  1. Front Matter
    Pages i-x
  2. Xiaoxin Liao
    Pages 1-26
  3. Xiaoxin Liao
    Pages 27-76
  4. Xiaoxin Liao
    Pages 77-93
  5. Xiaoxin Liao
    Pages 94-120
  6. Xiaoxin Liao
    Pages 145-167
  7. Back Matter
    Pages 169-178

About this book

Introduction

As is well-known, a control system always works under a variety of accidental or continued disturbances. Therefore, in designing and analysing the control system, stability is the first thing to be considered. Classic control theory was basically limited to a discussion of linear systems with constant coefficients. The fundamental tools for such studies were the Routh-Hurwitz algebraic criterion and the Nyquist geometric criterion. However, modern control theory mainly deals with nonlinear problems. The stability analysis of nonlinear control systems based on Liapunov stability theory can be traced back to the Russian school of stability. In 1944, the Russian mathematician Lurie, a specialist in control theory, discussed the stability of an autopilot. The well-known Lurie problem and the concept of absolute stability are presented, which is of universal significance both in theory and practice. Up until the end of the 1950's, the field of absolute stability was monopolized mainly by Russian scholars such as A. 1. Lurie, M. A. Aizeman, A. M. Letov and others. At the beginning of the 1960's, some famous American mathematicians such as J. P. LaSalle, S. Lefschetz and R. E. Kalman engaged themself in this field. Meanwhile, the Romanian scholar Popov presented a well-known frequency criterion and consequently ma de a decisive breakthrough in the study of absolute stability.

Keywords

Algebra boundary element method differential equation stability stability theory

Authors and affiliations

  • Xiaoxin Liao
    • 1
  1. 1.Department of Mathematics at HuazhongNormal UniversityWuhanPeople’s Republic of China

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-0608-7
  • Copyright Information Springer Science+Business Media B.V. 1993
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-017-0610-0
  • Online ISBN 978-94-017-0608-7
  • Series Print ISSN 0924-5952
  • Buy this book on publisher's site