Overview
- Provides the reader with a user-friendly framework for building Lyapunov functions in novel settings
- Helps the reader with feedback design and in quantifying the effects of system uncertainty
- Includes supplementary material: sn.pub/extras
Part of the book series: Communications and Control Engineering (CCE)
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Table of contents (12 chapters)
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Front Matter
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Background
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Front Matter
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Time-Invariant Case
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Front Matter
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Time-Varying Case
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Front Matter
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Systems with Multiple Time Scales
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Front Matter
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Back Matter
Keywords
About this book
Converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, but the functions it provides are often abstract and nonexplicit, and therefore may not lend themselves to engineering applications. Often, even when a system is known to be stable, one still needs explicit Lyapunov functions; however, once an appropriate strict Lyapunov function has been constructed, many robustness and stabilization problems can be solved through standard feedback designs or robustness arguments. Non-strict Lyapunov functions are often readily constructed.
This book contains a broad repertoire of Lyapunov constructions for nonlinear systems, focusing on methods for transforming non-strict Lyapunov functions into strict ones. Their explicitness and simplicity make them suitable for feedback design, and for quantifying the effects of uncertainty. Readers will benefit from the authors’ mathematical rigor and unifying, design-oriented approach, as well as the numerous worked examples.
Reviews
From the reviews:
“This monograph covers a wide range of nonlinear dynamical systems, including Jurdjevic-Quinn systems, time-varying systems satisfying LaSalle or Matrosov conditions, adaptively controlled dynamics, slowly and rapidly time-varying systems, and hybrid time-varying systems. … The book will be useful to researchers and graduate students in various areas of applied mathematics and control theory and engineering.” (Vladimir Sobolev, Zentralblatt MATH, Vol. 1186, 2010)
“This is an important and painstaking chore. … The book is a combination of a research monograph and an expository text. … those who need to analyze or to perform a detailed stability or stabilization analysis of concrete equations will find the book a very good source of ideas and references. … should be a desired addition to all libraries that serve mathematics departments and control engineering faculties. … could be used successfully as reading material for advanced graduate students interested in the subject matter.” (Zvi Artstein, SIAM Review, Vol. 53 (1), 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Constructions of Strict Lyapunov Functions
Authors: Michael Malisoff, Frédéric Mazenc
Series Title: Communications and Control Engineering
DOI: https://doi.org/10.1007/978-1-84882-535-2
Publisher: Springer London
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag London 2009
Hardcover ISBN: 978-1-84882-534-5Published: 30 June 2009
Softcover ISBN: 978-1-4471-5782-3Published: 30 October 2014
eBook ISBN: 978-1-84882-535-2Published: 13 June 2009
Series ISSN: 0178-5354
Series E-ISSN: 2197-7119
Edition Number: 1
Number of Pages: XVI, 386
Topics: Control and Systems Theory, Systems Theory, Control, Vibration, Dynamical Systems, Control, Control, Robotics, Mechatronics