Theory Of Associated Systems For Study Of The Stability In The Large
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Theory Of Associated Systems For Study Of The Stability In The Large
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Author : L. R. Borges Vieira
language : en
Publisher:
Release Date : 1965
Theory Of Associated Systems For Study Of The Stability In The Large written by L. R. Borges Vieira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Differential equations categories.
Stability Theory Of Switched Dynamical Systems
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Author : Zhendong Sun
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-06
Stability Theory Of Switched Dynamical Systems written by Zhendong Sun 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 2011-01-06 with Technology & Engineering categories.
There are plenty of challenging and interesting problems open for investigation in the field of switched systems. Stability issues help to generate many complex nonlinear dynamic behaviors within switched systems. The authors present a thorough investigation of stability effects on three broad classes of switching mechanism: arbitrary switching where stability represents robustness to unpredictable and undesirable perturbation, constrained switching, including random (within a known stochastic distribution), dwell-time (with a known minimum duration for each subsystem) and autonomously-generated (with a pre-assigned mechanism) switching; and designed switching in which a measurable and freely-assigned switching mechanism contributes to stability by acting as a control input. For each of these classes this book propounds: detailed stability analysis and/or design, related robustness and performance issues, connections to other control problems and many motivating and illustrative examples.
Stability And Stabilization Of Nonlinear Systems
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Author : Iasson Karafyllis
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-02
Stability And Stabilization Of Nonlinear Systems written by Iasson Karafyllis 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 2011-04-02 with Technology & Engineering categories.
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.
Stability Of Dynamical Systems
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2008
Stability Of Dynamical Systems written by 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 2008 with Differentiable dynamical systems categories.
In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.
Stability Elements Of The Theory And Application With Examples
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Author : Anatoliy A Martynyuk
language : en
Publisher: Sciendo
Release Date : 2020-12-20
Stability Elements Of The Theory And Application With Examples written by Anatoliy A Martynyuk and has been published by Sciendo this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-20 with categories.
This book is intended to familiarize the readers with basic concepts, and classic results of stability theory stated in a way as required by the rigorous rules of contemporary mathematics and, simultaneously, to introduce the learners to broad elds of not only the stability theory but also applications involved. The emphasis is put on various dynamical systems which are defined by different branches of science and through diverse areas of human activity but always with care not to exceed the basic classical approach in the presentation. All in all, the authors plan to combine the textbook-like with encyclopaedia-like content. Another special goal of the authors is to attract the reader's attention to those aspects of theories whose incomplete understanding may lead to inaccuracies or errors. Sometimes, anyway just as designed, the offered information is limited to the pure statements of facts without any proofs. The reader should consult the references to find out missing pieces of information. This book also makes use of numerical (computer) computations. Most of the material contained in the book has already been published, a large part in various works of the authors. Fragments of several chapters come from published works of other authors - some excerpts, particularly relating to basic concepts, and some classic results are taken from outside sources. The book is offered as a textbook for the college-level students or as an aid to the PhD students interested in practical problems of the stability theory. The prerequisites are not demanding - the basic knowledge of calculus, complex functions, and linear algebra which are covered in the suitable, elementary courses is required. The first two chapters include what is typically covered in most introductory courses for students. The first chapter contains definitions of various types of stability; the second commences classic stability theorems regarding ordinary differential equations, but the most basic, applicable in technical sciences. The linear equations are treated more broadly, which creates a foundation for the linear approximation of differential equations in the stability research. Chapter three deals with integral inequalities and their application to the stability studies. Integral inequalities, both linear and nonlinear, are effectively applied in the development of the direct Lyapunov method when the boundedness and stability of motion of nonlinear weakly coupled systems are studied. Chapter four is predominantly dedicated to the Lyapunov direct method. Still, some attention is also paid to the method of limiting equations because it can be used to study motion stability even in hopeless cases when other methods fail. The issue of constructing of the Lyapunov function is a key element in applications of the direct method, and this chapter provides several methods of constructing the function. In the end, a string of examples illustrating the use of the Lyapunov direct method is posted. Chapter five contains a detailed presentation of the comparison method and its use in the stability research. This method, being is essential part of the qualitative theory of equations, is particularly central in studies of largescale systems. In the method, some differential inequalities and Lyapunov functions allow nonlinear transformations of the original system to an equation (a system or a matrix system) of a lower dimension. The idea of delimiting and estimating so-called stability domains is developed in chapter six, where also a qualitative comparison of different stability procedures is made. The evaluation of the efficiency of various methods is conducted by applying, in each case, the same vector norm as a measure of the distance between solutions - no surprise the Lyapunov direct method wins the competition. The contrast between various method results is shown using an example of a simple second-order differential equation. Moreover, for linear systems, the notion of the best Lyapunov function is made. Manifolds of non-holonomic equations of motion are in the focus of chapter seven. Application of topological manifolds and mapping techniques prove to be effective tools in the stability research that extends more and more to advanced fields of mathematics. The chapter reviews specific applications of the Lyapunov direct method to investigations of invariant manifolds and some practical results of the topological fixed point theory. Chapter eight deals with recurrence equations, difference equations, and difference inequalities that mainly are associated with discrete dynamic systems. These types of models are usually obtained by converting the time-continuous dynamics into discrete-time dynamics by employing the Poincare-type mappings. The main objective is the stability investigation of solutions and its estimates. Chapter nine is limited to a short overview of some stability issues for delay differential equations modelling some practical processes and systems with aftereffect phenomena - the main worry is about the compensation for the loss of stability due to delay in the system. Linear models are discussed, but the emphasis is put on Lyapunov functionals for nonlinear equations. Chapter ten on partial differential equations, not including the means of discretization to the stability analysis, uses an approach based on the utilization Lyapunov functionals. The Lyapunov theory is exercised here in relation to a particular class of continuous models - it is an outline of some techniques rather than the methodology. The presented here approach is anecdotal, and it is based on specific cases and examples. Chapter eleven presents some samples of the probabilistic approach to stability matters. This category of problems is necessary when in the modelling process, it turns out that the excitations are not clear, not defined, or not repeatable. In the present considerations, the stability study is reduced to examining the stability of the trivial solution, and the focus is on the almost-sure probability. The last chapter provides a brief introduction to themes of chaos, focusing on the dependence of chaos on the Lyapunov exponent. The irregular behaviour of solutions of motion which is identified with chaos is not due to stochastic forcing or sensitive dependence on initial conditions. The real reason for it is the exponential rate of the distance between the trajectories due to nonlinearities of the system - the Lyapunov exponent is a measure of it.
What Is Stability Theory Of Large Scale Dynamical Systems
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Author : Reece A. Kay
language : en
Publisher: CreateSpace
Release Date : 2015-01-31
What Is Stability Theory Of Large Scale Dynamical Systems written by Reece A. Kay and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-31 with Mathematics categories.
What is Stability Theory-of Large-scale Dynamical Systems is one of the series of books covering various topics of science, technology and management published by London School of Management Studies. The book will cover the introduction to the Topic and can be used as a very useful course study material for students pursuing their studies in undergraduate and graduate levels in universities and colleges and those who want to learn the topic in brief via a short and complete resource. We hope you find this book useful is shaping your future career, Please send us your enquiries related to our publications to [email protected] London School of Management Studies www.lsms.org.uk
Stability Theory Of Dynamical Systems
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Author : Jacques Leopold Willems
language : en
Publisher: Wiley-Interscience
Release Date : 1970
Stability Theory Of Dynamical Systems written by Jacques Leopold Willems and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Science categories.
Consepts Of Stability Theory Of Large Scale Dynamical Systems
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Author : Leo H. Doyle
language : en
Publisher: CreateSpace
Release Date : 2015-01-31
Consepts Of Stability Theory Of Large Scale Dynamical Systems written by Leo H. Doyle and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-31 with Science categories.
Consepts of Stability Theory-of Large-scale Dynamical Systems is one of the series of books covering various topics of science, technology and management published by London School of Management Studies. The book will cover the introduction to the Topic and can be used as a very useful course study material for students pursuing their studies in undergraduate and graduate levels in universities and colleges and those who want to learn the topic in brief via a short and complete resource. We hope you find this book useful is shaping your future career, Please send us your enquiries related to our publications to [email protected] London School of Management Studies www.lsms.org.uk
Nonlinear Systems
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Author : Shankar Sastry
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Nonlinear Systems written by Shankar Sastry 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 2013-04-18 with Mathematics categories.
There has been much excitement over the emergence of new mathematical techniques for the analysis and control of nonlinear systems. In addition, great technological advances have bolstered the impact of analytic advances and produced many new problems and applications which are nonlinear in an essential way. This book lays out in a concise mathematical framework the tools and methods of analysis which underlie this diversity of applications.
Stability Theory Of Large Scale Dynamical Systems Course Book
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Author : Matilda R. Khan
language : en
Publisher: CreateSpace
Release Date : 2015-01-31
Stability Theory Of Large Scale Dynamical Systems Course Book written by Matilda R. Khan and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-31 with Mathematics categories.
Stability Theory-of Large-scale Dynamical Systems Course Book is one of the series of books covering various topics of science, technology and management published by London School of Management Studies. The book will cover the introduction to the Topic and can be used as a very useful course study material for students pursuing their studies in undergraduate and graduate levels in universities and colleges and those who want to learn the topic in brief via a short and complete resource. We hope you find this book useful is shaping your future career, Please send us your enquiries related to our publications to [email protected] London School of Management Studies www.lsms.org.uk