Download or read book Stability Analysis of Nonlinear Systems written by Vangipuram Lakshmikantham and published by Birkhäuser. This book was released on 2015-12-29 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonlinear Systems Stability Analysis written by Seyed Kamaleddin Yadavar Nikravesh and published by CRC Press. This book was released on 2018-09-03 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stability Analysis and Nonlinear Observer Design using Takagi Sugeno Fuzzy Models written by Zsófia Lendek and published by Springer Science & Business Media. This book was released on 2010-10-27 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in decision making, monitoring, fault detection, and control require the knowledge of state variables and time-varying parameters that are not directly measured by sensors. In such situations, observers, or estimators, can be employed that use the measured input and output signals along with a dynamic model of the system in order to estimate the unknown states or parameters. An essential requirement in designing an observer is to guarantee the convergence of the estimates to the true values or at least to a small neighborhood around the true values. However, for nonlinear, large-scale, or time-varying systems, the design and tuning of an observer is generally complicated and involves large computational costs. This book provides a range of methods and tools to design observers for nonlinear systems represented by a special type of a dynamic nonlinear model -- the Takagi--Sugeno (TS) fuzzy model. The TS model is a convex combination of affine linear models, which facilitates its stability analysis and observer design by using effective algorithms based on Lyapunov functions and linear matrix inequalities. Takagi--Sugeno models are known to be universal approximators and, in addition, a broad class of nonlinear systems can be exactly represented as a TS system. Three particular structures of large-scale TS models are considered: cascaded systems, distributed systems, and systems affected by unknown disturbances. The reader will find in-depth theoretic analysis accompanied by illustrative examples and simulations of real-world systems. Stability analysis of TS fuzzy systems is addressed in detail. The intended audience are graduate students and researchers both from academia and industry. For newcomers to the field, the book provides a concise introduction dynamic TS fuzzy models along with two methods to construct TS models for a given nonlinear system

Download or read book Nonlinear Instability Analysis written by Lokenath Debnath and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability Analysis of Nonlinear Microwave Circuits written by Almudena Suárez and published by Artech House. This book was released on 2003 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation "Stability Analysis of Nonlinear Microwave Circuits is essential reading for microwave designers working with circuits based on solid state devices, diodes, and transistors, engineers designing radio-frequency circuits, and professionals regularly involved in any area requiring a functional knowledge of nonlinear oscillations and stability concepts. It provides an in-depth look at the very complex and often unforeseen behavior of nonlinear circuits. The book includes detailed coverage of power amplifiers, voltage-controlled oscillators, frequency dividers, frequency multipliers, self-oscillating mixers, and phased-locked loops."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

Download or read book Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems written by V. Lakshmikantham and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Studies in Non Linear Stability Theory written by Wiktor Eckhaus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-linear stability problems formulated in terms of non-linear partial differential equations have only recently begun to attract attention and it will probably take some time before our understanding of those problems reaches some degree of maturity. The passage from the more classical linear analysis to a non-linear analysis increases the mathematical complexity of the stability theory to a point where it may become discouraging, while some of the more usual mathematical methods lose their applicability. Although considerable progress has been made in recent years, notably in the field of fluid mechanics, much still remains to be done before a more permanent outline of the subject can be established. I have not tried to present in this monograph an account of what has been accomplished, since the rapidly changing features of the field make the periodical literature a more appropriate place for such a review. The aim of this book is to present one particular line of research, originally developed in a series of papers published in 'Journal de Mecanique' 1962-1963, in which I attempted to construct a mathematical theory for certain classes of non-linear stability problems, and to gain some understanding of the non-linear phenomena which are involved. The opportunity to collect the material in this volume has permitted a more coherent presentation, while various points of the analysis have been developed in greater detaiL I hope that a more unified form of the theory has thus been achieved.

Download or read book Nonlinear Systems Analysis written by M. Vidyasagar and published by SIAM. This book was released on 2002-01-01 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.

Download or read book Nonlinear Analysis of Thin Walled Structures written by James F. Doyle and published by Springer Science & Business Media. This book was released on 2001-05-11 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanical engineering, an engineering discipline born of the needs of the Industrial Revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face the profound issues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a new series, featuring graduate texts and research monographs, intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that will cover a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consult ing editors are listed on page vi. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. We are pleased to present Nonlinear Analysis of Thin-Walled Structures by James F. Doyle. Austin, Texas Frederick F. Ling Preface This book is concerned with the challenging subject of the nonlinear static, dynamic, and stability analyses of thin-walled structures. It carries on from where Static and Dynamic Analysis of Structures, published by Kluwer 1991, left off; that book concentrated on frames and linear analysis, while the present book is focused on plated structures, nonlinear analysis, and a greater emphasis on stability analysis.

Download or read book Stability and Stabilization of Nonlinear Systems written by Iasson Karafyllis and published by Springer Science & Business Media. This book was released on 2011-04-02 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of their stability and feedback stabilization which enables the reader to learn and understand major techniques used in mathematical control theory. In particular: the important techniques of proving global stability properties are presented closely linked with corresponding methods of nonlinear feedback stabilization; a general framework of methods for proving stability is given, thus allowing the study of a wide class of nonlinear systems, including finite-dimensional systems described by ordinary differential equations, discrete-time systems, systems with delays and sampled-data systems; approaches to the proof of classical global stability properties are extended to non-classical global stability properties such as non-uniform-in-time stability and input-to-output stability; and new tools for stability analysis and control design of a wide class of nonlinear systems are introduced. The presentational emphasis of Stability and Stabilization of Nonlinear Systems is theoretical but the theory’s importance for concrete control problems is highlighted with a chapter specifically dedicated to applications and with numerous illustrative examples. Researchers working on nonlinear control theory will find this monograph of interest while graduate students of systems and control can also gain much insight and assistance from the methods and proofs detailed in this book.

Download or read book Nonlinear Analysis written by Themistocles M Rassias and published by World Scientific. This book was released on 1988-01-01 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Fixed Point Theory and Nonlinear Problems (Th Rassias)Global Linearization Iterative Methods and Nonlinear Partial Differential Equations III (M Altman)On Generalized Power Series and Generalized Operational Calculus and Its Application (M Al-Bassam)Multiple Solutions to Parametrized Nonlinear Differential Systems from Nielsen Fixed Point Theory (R Brown)The topology of Ind-Affine Sets (P Cherenack)Almost Approximately Polynomial Functions (P Cholewa)Cohomology Classes and Foliated Manifolds (M Craioveanu & M Puta)Bifurcation and Nonlinear Instability in Applied Mathematics (L Debnath)The Stability of Weakly Additive Functional (H Drljevic)Index Theory for G-Bundle Pairs with Applications to Borsuk-Ulam Type Theorems for G-Sphere Bundles (E Fadell & S Husseini)Nonlinear Approximation and Moment Problem (J S Hwang & G D Lin)Periods in Equicontinuous Topological Dynamical Systems (A Iwanik et al.)Continuation Theorems for Semi-Linear Equations in Banach Spaces: A Survey (J Mawhin & K Rybakowski)On Contractifiable Self-Mappings (P Meyers)Normal Structures and Nonexpansive Mappings in Banach Spaces (J Nelson et al.): Survey on Uniqueness and Classification Theorems for Minimal Surfaces (Th Rassias)Contractive Definitions (B Rhoades)On KY Fan's Theorem and Its Applications (S Singh)Fixed Points of Amenable Semigroups of Differentiable Operators (P Soardi)Research Problems on Nonlinear Equations (Th Rassias) Readership: Mathematicians and applied scientists. Keywords:Nonlinear Analysis;Nonlinear Partial Differential Equations III;Polynomial Functions;Cohomology Classes;Foliated Manifolds;Topological Dynamical Systems;Minimal Surfaces;Differentiable Operators;Nonlinear Equations

Download or read book Hydrodynamics and Nonlinear Instabilities written by Claude Godrèche and published by Cambridge University Press. This book was released on 2005-07-21 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents five sets of pedagogical lectures by internationally respected researchers on nonlinear instabilities and the transition to turbulence in hydrodynamics. The book begins with a general introduction to hydrodynamics covering fluid properties, flow measurement, dimensional analysis and turbulence. Chapter two reviews the special characteristics of instabilities in open flows. Chapter three presents mathematical tools for multiscale analysis and asymptotic matching applied to the dynamics of fronts and localized nonlinear states. Chapter four gives a detailed review of pattern forming instabilities. The final chapter provides a detailed and comprehensive introduction to the instability of flames, shocks and detonations. Together, these lectures provide a thought-provoking overview of current research in this important area.

Download or read book Nonlinear Stability and Bifurcation Theory written by Hans Troger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every student in engineering or in other fields of the applied sciences who has passed through his curriculum knows that the treatment of nonlin ear problems has been either avoided completely or is confined to special courses where a great number of different ad-hoc methods are presented. The wide-spread believe that no straightforward solution procedures for nonlinear problems are available prevails even today in engineering cir cles. Though in some courses it is indicated that in principle nonlinear problems are solveable by numerical methods the treatment of nonlinear problems, more or less, is considered to be an art or an intellectual game. A good example for this statement was the search for Ljapunov functions for nonlinear stability problems in the seventies. However things have changed. At the beginning of the seventies, start ing with the work of V.1. Arnold, R. Thom and many others, new ideas which, however, have their origin in the work of H. Poincare and A. A. Andronov, in the treatment of nonlinear problems appeared. These ideas gave birth to the term Bifurcation Theory. Bifurcation theory allows to solve a great class of nonlinear problems under variation of parameters in a straightforward manner.

Download or read book Introduction to Sensitivity and Stability Analysis in Nonlinear Programming written by Fiacco and published by Academic Press. This book was released on 1983-11-02 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Sensitivity and Stability Analysis in Nonlinear Programming

Download or read book Nonlinear Dirac Equation Spectral Stability of Solitary Waves written by Nabile Boussaïd and published by American Mathematical Soc.. This book was released on 2019-11-21 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.

Download or read book Spectral and Dynamical Stability of Nonlinear Waves written by Todd Kapitula and published by Springer Science & Business Media. This book was released on 2013-06-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability.

Download or read book The Analysis of Linear and Nonlinear Instability Phenomena in Heated Channels written by J. L. Achard and published by . This book was released on 1980 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: