Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems

Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems PDF

Author: V. Lakshmikantham

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 182

ISBN-13: 9401579393

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One service mathematics has rendered the 'Et moi, "', si j'avait su comment en revenir, je n'y serais point all".' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . .'; 'One service logic has rendered com puter science . .'; 'One service category theory has rendered mathematics . .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Stability Analysis of Nonlinear Systems

Stability Analysis of Nonlinear Systems PDF

Author: Vangipuram Lakshmikantham

Publisher: Birkhäuser

Published: 2015-12-29

Total Pages: 339

ISBN-13: 3319272004

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The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.

Nonlinear Systems Stability Analysis

Nonlinear Systems Stability Analysis PDF

Author: Seyed Kamaleddin Yadavar Nikravesh

Publisher: CRC Press

Published: 2017-10-12

Total Pages: 319

ISBN-13: 9781138072770

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The equations used to describe dynamic properties of physical systems are often nonlinear, and it is rarely possible to find their solutions. Although numerical solutions are impractical and graphical techniques are not useful for many types of systems, there are different theorems and methods that are useful regarding qualitative properties of nonlinear systems and their solutions¿system stability being the most crucial property. Without stability, a system will not have value. Nonlinear Systems Stability Analysis: Lyapunov-Based Approach introduces advanced tools for stability analysis of nonlinear systems. It presents the most recent progress in stability analysis and provides a complete review of the dynamic systems stability analysis methods using Lyapunov approaches. The author discusses standard stability techniques, highlighting their shortcomings, and also describes recent developments in stability analysis that can improve applicability of the standard methods. The text covers mostly new topics such as stability of homogonous nonlinear systems and higher order Lyapunov functions derivatives for stability analysis. It also addresses special classes of nonlinear systems including time-delayed and fuzzy systems. Presenting new methods, this book provides a nearly complete set of methods for constructing Lyapunov functions in both autonomous and nonautonomous systems, touching on new topics that open up novel research possibilities. Gathering a body of research into one volume, this text offers information to help engineers design stable systems using practice-oriented methods and can be used for graduate courses in a range of engineering disciplines.

Nonlinear Dynamical Systems and Control

Nonlinear Dynamical Systems and Control PDF

Author: Wassim M. Haddad

Publisher: Princeton University Press

Published: 2008-02-17

Total Pages: 975

ISBN-13: 0691133298

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The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics and beyond. This book presents and develops a complete and thorough treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods.

Weakly Connected Nonlinear Systems

Weakly Connected Nonlinear Systems PDF

Author: Anatoly Martynyuk

Publisher: CRC Press

Published: 2019-08-30

Total Pages: 228

ISBN-13: 9780367380632

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Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected equations. After supplying the necessary mathematical foundation, the book illustrates recent approaches to studying the boundedness of motion of weakly connected nonlinear systems. The authors consider conditions for asymptotic and uniform stability using the auxiliary vector Lyapunov functions and explore the polystability of the motion of a nonlinear system with a small parameter. Using the generalization of the direct Lyapunov method with the asymptotic method of nonlinear mechanics, they then study the stability of solutions for nonlinear systems with small perturbing forces. They also present fundamental results on the boundedness and stability of systems in Banach spaces with weakly connected subsystems through the generalization of the direct Lyapunov method, using both vector and matrix-valued auxiliary functions. Designed for researchers and graduate students working on systems with a small parameter, this book will help readers get up to date on the knowledge required to start research in this area.

Variable Structure and Lyapunov Control

Variable Structure and Lyapunov Control PDF

Author: Alan S.I. Zinober

Publisher: Springer

Published: 1993-12-15

Total Pages: 0

ISBN-13: 9783540198697

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This book covers a wide range of up-to-date sliding mode Variable Structure Control (VSC) and Lyapunov Control research and design techniques for the robust control of uncertain systems. In direct contrast to most adaptive controllers, these deterministic controllers employ fixed nonlinear feedback control functions, which operate effectively over a specified magnitude range of system parameter variations and disturbances. There are 18 chapters covering and discussing such topics as the theoretical and practical design of controllers for uncertain multivariable systems, novel algebraic approaches for sliding mode control, discrete-time control, and the stabilizing VSC of uncertain infinite-dimensional systems. The main areas of application include electric motor drives, robotics, flight control and space systems, as well as power electronics and chemical processes, some of which are described in the book.

Stability and Stabilization of Nonlinear Systems

Stability and Stabilization of Nonlinear Systems PDF

Author: Dirk Aeyels

Publisher: Springer

Published: 2008-01-26

Total Pages: 394

ISBN-13: 1846285771

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These papers were presented at the first EC-TMR Nonlinear Control Network Workshop, on Stability and Stabilization of Nonlinear Systems, that took place in March 1999, Ghent, Belgium. The TMR programme offers a unique opportunity for the academic community to expand their knowledge, share their experience and identify and discuss strategic issues in aspects of nonlinear control engineering. The aim is to create a resource centre of available expertise and research interests. This outstanding reference volume presents current and emerging research directions, including: Stability analysis of nonlinear dynamical systems and converse Lyapunov theorems; Stabilization and regulation of nonlinear dynamical control systems; Control of physical systems using physics-based Lyapunov functions and passivity, as well as bifurcation analysis and optimal control. This collection of peer-reviewed papers provides a comprehensive overview of this field of research for graduate students and researchers in engineering and applied mathematics.

Robust Nonlinear Control Design

Robust Nonlinear Control Design PDF

Author: Randy Freeman

Publisher: Springer Science & Business Media

Published: 2008-01-11

Total Pages: 268

ISBN-13: 0817647589

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This softcover book summarizes Lyapunov design techniques for nonlinear systems and raises important issues concerning large-signal robustness and performance. The authors have been the first to address some of these issues, and they report their findings in this text. The researcher who wishes to enter the field of robust nonlinear control could use this book as a source of new research topics. For those already active in the field, the book may serve as a reference to a recent body of significant work. Finally, the design engineer faced with a nonlinear control problem will benefit from the techniques presented here.

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