Authors:
- This book will answer the question; “what is sufficient and necessary condition for the absolute stability of the Lurie problem?” This is a question that has not been solved in 60 years.
- The new ideas and methodology within this book can be generalized to solve stability problems of other types of nonlinear systems
Part of the book series: Mathematical Modelling: Theory and Applications (MMTA, volume 25)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
About this book
Following the recent developments in the field of absolute stability, Prof. Xiaoxin Liao, in conjunction with Prof. Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and 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 book is aimed to be used by undergraduates in the areas of applied mathematics, nonlinear control systems, and chaos control and synchronisation, but may also be useful as a reference 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 a prerequisite.
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)
Authors and Affiliations
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Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China
Xiaoxin Liao
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Department of Applied Mathematics, University of Western Ontario, London, Canada
Pei Yu
Bibliographic Information
Book Title: Absolute Stability of Nonlinear Control Systems
Authors: Xiaoxin Liao, Pei Yu
Series Title: Mathematical Modelling: Theory and Applications
DOI: https://doi.org/10.1007/978-1-4020-8482-9
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2008
Hardcover ISBN: 978-1-4020-8481-2Published: 25 August 2008
Softcover ISBN: 978-90-481-7892-6Published: 23 November 2010
eBook ISBN: 978-1-4020-8482-9Published: 16 July 2008
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: Ordinary Differential Equations, Systems Theory, Control, Vibration, Dynamical Systems, Control, Applications of Mathematics