Mathematical Modelling: Theory and Applications

Absolute Stability of Nonlinear Control Systems

Authors: Liao, Xiaoxin, Yu, Pei

  • Answers a question that has not been solved in more than 60 years: what is sufficient and necessary condition for the absolute stability of the Lurie problem?
  • Includes new ideas and methodology that can be generalized to solve stability problems of other types of nonlinear systems
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eBook $89.00
price for USA (gross)
  • ISBN 978-1-4020-8482-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-1-4020-8481-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-90-481-7892-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

Following the recent developments in the field of absolute stability, Professor Xiaoxin Liao, in conjunction with Professor Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and the Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This includes nonlinear control systems with multiple controls, interval control systems, time-delay and neutral Lurie control systems, systems described by functional differential equations, the absolute stability for neural networks, as well as applications to chaos control and chaos synchronization.

This book is aimed at undergraduates and lecturers in the areas of applied mathematics, nonlinear control systems and chaos control and synchronisation, but may also be useful as a reference work for researchers and engineers. The book is self-contained, though a basic knowledge of calculus, linear system and matrix theory, and ordinary differential equations is required to gain a complete understanding of the workings and methodologies discussed within.

Reviews

From the reviews of the second edition:

"This monograph is devoted to stability problems of linear systems with nonlinear feedbacks … . The monograph is written in a very clear style. It contains many new ideas and it will certainly be useful as a reference work for engineers." (Stanislaw Sedziwy, Mathematical Reviews, Issue 2009 m)

“This book is based heavily on material developed by the authors and is aimed at graduate students and advanced undergraduates. The book begins with an introduction to Lurie control systems, and algebraic sufficient conditions for the absolute stability of several classes of Lurie-type systems are developed. Recent developments are then presented, including results for systems with multiple controls, interval systems, time-delay and neutral Lurie control systems, neural networks, and applications to chaos control and synchronization.” (IEEE Control Systems Magazine, Vol. 29, October, 2009)


Table of contents (13 chapters)

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-1-4020-8482-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-1-4020-8481-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-90-481-7892-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Absolute Stability of Nonlinear Control Systems
Authors
Series Title
Mathematical Modelling: Theory and Applications
Series Volume
25
Copyright
2008
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-8482-9
DOI
10.1007/978-1-4020-8482-9
Hardcover ISBN
978-1-4020-8481-2
Softcover ISBN
978-90-481-7892-6
Series ISSN
1386-2960
Edition Number
2
Number of Pages
XII, 384
Additional Information
Originally published as volume 5 in the series: Mathematics and its Applications
Topics