Discontinuous Systems
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Discontinuous Systems
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Author : Yury V. Orlov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-28
Discontinuous Systems written by Yury V. Orlov 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 2008-10-28 with Technology & Engineering categories.
Discontinuous Systems develops nonsmooth stability analysis and discontinuous control synthesis based on novel modeling of discontinuous dynamic systems, operating under uncertain conditions. While being primarily a research monograph devoted to the theory of discontinuous dynamic systems, no background in discontinuous systems is required; such systems are introduced in the book at the appropriate conceptual level. Being developed for discontinuous systems, the theory is successfully applied to their subclasses – variable-structure and impulsive systems – as well as to finite- and infinite-dimensional systems such as distributed-parameter and time-delay systems. The presentation concentrates on algorithms rather than on technical implementation although theoretical results are illustrated by electromechanical applications. These specific applications complete the book and, together with the introductory theoretical constituents bring some elements of the tutorial to the text.
Principles Of Discontinuous Dynamical Systems
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Author : Marat Akhmet
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-26
Principles Of Discontinuous Dynamical Systems written by Marat Akhmet 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 2010-08-26 with Mathematics categories.
Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whose solutions have prescribed moments of impulses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progresses systematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last two chapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems.
Discontinuous Dynamical Systems On Time Varying Domains
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Author : Albert C. J. Luo
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-06
Discontinuous Dynamical Systems On Time Varying Domains written by Albert C. J. Luo 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 2009-11-06 with Science categories.
"Discontinuous Dynamical Systems on Time-varying Domains" is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains, this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed. From such a theory, principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time-varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers, advanced undergraduate and graduate students in mathematics, physics and mechanics. Dr. Albert C. J. Luo is a professor at Southern Illinois University Edwardsville, USA. His research is involved in the nonlinear theory of dynamical systems. His main contributions are in the following aspects: a stochastic and resonant layer theory in nonlinear Hamiltonian systems, singularity on discontinuous dynamical systems, and approximate nonlinear theories for a deformable-body.
Vibration Of Strongly Nonlinear Discontinuous Systems
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Author : V.I. Babitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-02
Vibration Of Strongly Nonlinear Discontinuous Systems written by V.I. Babitsky 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 2012-11-02 with Technology & Engineering categories.
Among the wide diversity of nonlinear mechanical systems, it is possible to distinguish a representative class of the systems which may be characterised by the presence of threshold nonlinear positional forces. Under particular configurations, such systems demonstrate a sudden change in the behaviour of elastic and dissipative forces. Mathematical study of such systems involves an analysis of equations of motion containing large-factored nonlinear terms which are associated with the above threshold nonlinearity. Due to this, we distinguish such discontinuous systems from the much wider class of essentially nonlinear systems, and define them as strongly nonlinear systems'. The vibration occurring in strongly nonlinear systems may be characterised by a sudden and abrupt change of the velocity at particular time instants. Such a vibration is said to be non-smooth. The systems most studied from this class are those with relaxation (Van Der Pol, Andronov, Vitt, Khaikhin, Teodorchik, etc. [5,65,70,71,98,171,181]), where the non-smooth vibration usually appears due to the presence of large nonconservative nonlinear forces. Equations of motion describing the vibration with relaxation may be written in such a manner that the highest derivative is accompanied by a small parameter. The methods of integration of these equations have been developed by Vasilieva and Butuzov [182], Volosov and Morgunov [190], Dorodnitsin [38], Zheleztsov [201], Mischenko and Rozov [115], Pontriagin [137], Tichonov [174,175], etc. In a system with threshold nonlinearity, the non-smooth vibration occurs due to the action of large conservative forces. This is distinct from a system with relaxation.
Discontinuous Dynamics And System Synchronization
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Author : Fuhong Min
language : en
Publisher: Springer Nature
Release Date : 2024-08-11
Discontinuous Dynamics And System Synchronization written by Fuhong Min and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-11 with Science categories.
This book provides a systematic introduction to the dynamical behaviors of discontinuous dynamical systems and system synchronization. The first part of the book presents the theory of flow switching in discontinuous dynamical systems as well as the switching dynamics in such discontinuous systems. The second part presents a theory for interaction discontinuities between distinct dynamical systems, from which partial and complete chaotic synchronizations in such systems are studied analytically and experimentally.
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.
System Dynamics With Interaction Discontinuity
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Author : Albert C. J. Luo
language : en
Publisher: Springer
Release Date : 2015-07-08
System Dynamics With Interaction Discontinuity written by Albert C. J. Luo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-08 with Technology & Engineering categories.
This book describes system dynamics with discontinuity caused by system interactions and presents the theory of flow singularity and switchability at the boundary in discontinuous dynamical systems. Based on such a theory, the authors address dynamics and motion mechanism of engineering discontinuous systems due to interaction. Stability and bifurcations of fixed points in nonlinear discrete dynamical systems are presented, and mapping dynamics are developed for analytical predictions of periodic motions in engineering discontinuous dynamical systems. Ultimately, the book provides an alternative way to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.
Stability Of Stationary Sets In Control Systems With Discontinuous Nonlinearities
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Author : Vladimir Andreevich I?A?kubovich
language : en
Publisher: World Scientific
Release Date : 2004
Stability Of Stationary Sets In Control Systems With Discontinuous Nonlinearities written by Vladimir Andreevich I?A?kubovich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the KalmanOCoYakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines. Sample Chapter(s). Chapter 1: Foundations of Theory of Differential Equations with Discontinuous Right-Hand Sides (455 KB). Contents: Foundations of Theory of Differential Equations with Discontinuous Right-Hand Sides; Auxiliary Algebraic Statements on Solutions of Matrix Inequalities of a Special Type; Dichotomy and Stability of Nonlinear Systems with Multiple Equilibria; Stability of Equilibria Sets of Pendulum-Like Systems. Readership: Upper level undergraduates, graduate students, academics, researchers and engineers involved with mechanics, electrical science and power systems."
Bifurcation And Chaos In Discontinuous And Continuous Systems
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Author : Michal Fečkan
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-30
Bifurcation And Chaos In Discontinuous And Continuous Systems written by Michal Fečkan 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 2011-05-30 with Science categories.
"Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving difference equations, ordinary and partial differential equations, differential equations with impulses, piecewise smooth differential equations, differential and difference inclusions, and differential equations on infinite lattices as well. This book is intended for mathematicians, physicists, theoretically inclined engineers and postgraduate students either studying oscillations of nonlinear mechanical systems or investigating vibrations of strings and beams, and electrical circuits by applying the modern theory of bifurcation methods in dynamical systems. Dr. Michal Fečkan is a Professor at the Department of Mathematical Analysis and Numerical Mathematics on the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovakia. He is working on nonlinear functional analysis, bifurcation theory and dynamical systems with applications to mechanics and vibrations.
Singularity And Dynamics On Discontinuous Vector Fields
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Author : Albert C.J. Luo
language : en
Publisher: Elsevier
Release Date : 2006-07-07
Singularity And Dynamics On Discontinuous Vector Fields written by Albert C.J. Luo and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-07 with Science categories.
This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional Newton mechanics. The new ideas and concepts will stimulate ones' thought and creativities in corresponding subjects. The author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in dynamics. - Challenging continuous Newton's dynamics - Original theory and seeds of new researches in the field - Wide spectrum of applications in science and engineering - Systematic presentation and clear illustrations