Technical Report No328 On The Construction Of Lyapunov Functions For Nonlinear Systems
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Technical Report No328 On The Construction Of Lyapunov Functions For Nonlinear Systems
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Author : United States. Naval Research Office
language : en
Publisher:
Release Date : 1960
Technical Report No328 On The Construction Of Lyapunov Functions For Nonlinear Systems written by United States. Naval Research Office and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with categories.
On The Construction Of Lyapunov Functions For Nonlinear Systems
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Author : K. S. NARENDRA
language : en
Publisher:
Release Date : 1960
On The Construction Of Lyapunov Functions For Nonlinear Systems written by K. S. NARENDRA and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with categories.
Constructions Of Strict Lyapunov Functions
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Author : Michael Malisoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-13
Constructions Of Strict Lyapunov Functions written by Michael Malisoff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-13 with Technology & Engineering categories.
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.
Vector Lyapunov Functions And Stability Analysis Of Nonlinear Systems
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Author : V. Lakshmikantham
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Vector Lyapunov Functions And Stability Analysis Of Nonlinear Systems written by V. Lakshmikantham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Nonlinear Systems Stability Analysis
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Author : Seyed Kamaleddin Yadavar Nikravesh
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Nonlinear Systems Stability Analysis written by Seyed Kamaleddin Yadavar Nikravesh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Science categories.
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.
On A Class Of Nonlinear Systems And Its Lyapunov Functions
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Author : Y-F. Lam
language : en
Publisher:
Release Date : 1974
On A Class Of Nonlinear Systems And Its Lyapunov Functions written by Y-F. Lam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Lyapunov functions categories.
Nonlinear System Analysis And Synthesis Part I Study Of Lyapunov Functions For Problems Of Control And Of Optimality Of Linear Systems
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Author : R. E. Kalman
language : en
Publisher:
Release Date : 1964
Nonlinear System Analysis And Synthesis Part I Study Of Lyapunov Functions For Problems Of Control And Of Optimality Of Linear Systems written by R. E. Kalman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.
Research covered in this report may be broken into four parts. I. Lyapunov Function for the Problem of Lur'e in Automatic Control. This problem is completely resolved by giving conditions for the existence of a Lyapunov function and an algorithm for its construction. II. On Polynomial Lyapunov Function. A preliminary study of the use of polynomial Lyapunov functions in the study of stability, with particular attention to possible computational utilization. III. When is a Linear Control System Optimal. Discussion of the problem: Given a control law, for what performance indices is it optimal. This treatment involves the use of frequency domain techniques. IV. ASP Modifications. A description of changes and proposed changes in the ASP Program. This program is more completely described in ASD-TR-61-27, Volume I and II. (Author).
Construction Of Global Lyapunov Functions Using Radial Basis Functions
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Author : Peter Giesl
language : en
Publisher: Springer
Release Date : 2007-04-11
Construction Of Global Lyapunov Functions Using Radial Basis Functions written by Peter Giesl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-11 with Mathematics categories.
The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.
Nonsmooth Lyapunov Analysis In Finite And Infinite Dimensions
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Author : Yury Orlov
language : en
Publisher: Springer Nature
Release Date : 2020-02-08
Nonsmooth Lyapunov Analysis In Finite And Infinite Dimensions written by Yury Orlov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-08 with Technology & Engineering categories.
Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions provides helpful tools for the treatment of a broad class of dynamical systems that are governed, not only by ordinary differential equations but also by partial and functional differential equations. Existing Lyapunov constructions are extended to discontinuous systems—those with variable structure and impact—by the involvement of nonsmooth Lyapunov functions. The general theoretical presentation is illustrated by control-related applications; the nonsmooth Lyapunov construction is particularly applied to the tuning of sliding-mode controllers in the presence of mismatched disturbances and to orbital stabilization of the bipedal gate. The nonsmooth construction is readily extendible to the control and identification of distributed-parameter and time-delay systems. The first part of the book outlines the relevant fundamentals of benchmark models and mathematical basics. The second concentrates on the construction of nonsmooth Lyapunov functions. Part III covers design and applications material. This book will benefit the academic research and graduate student interested in the mathematics of Lyapunov equations and variable-structure control, stability analysis and robust feedback design for discontinuous systems. It will also serve the practitioner working with applications of such systems. The reader should have some knowledge of dynamical systems theory, but no background in discontinuous systems is required—they are thoroughly introduced in both finite- and infinite-dimensional settings.
The Analysis Of Nonlinear Sampled Data Control Systems Using Lyapunov S Second Method
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Author : Gary Louis Blank
language : en
Publisher:
Release Date : 1963
The Analysis Of Nonlinear Sampled Data Control Systems Using Lyapunov S Second Method written by Gary Louis Blank and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Automatic control categories.