Stability of Dynamical Systems Book

Stability of Dynamical Systems


  • Author : Anthony N. Michel
  • Publisher : Springer Science & Business Media
  • Release Date : 2008
  • Genre: Language Arts & Disciplines
  • Pages : 501
  • ISBN 10 : 9780817644864

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Stability of Dynamical Systems Excerpt :

Filling a gap in the literature, this volume offers the first comprehensive analysis of all the major types of system models. Throughout the text, there are many examples and applications to important classes of systems in areas such as power and energy, feedback control, artificial neural networks, digital signal processing and control, manufacturing, computer networks, and socio-economics. 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 a huge variety of fields.

Stability of Dynamical Systems Book

Stability of Dynamical Systems


  • Author : Xiaoxin Liao
  • Publisher : Elsevier
  • Release Date : 2007-08-01
  • Genre: Mathematics
  • Pages : 718
  • ISBN 10 : 0080550614

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Stability of Dynamical Systems Excerpt :

The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems. Presents comprehensive theory and methodology of stability analysis Can be used as textbook for graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, scientific computation Serves as a comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers

Global Stability of Dynamical Systems Book

Global Stability of Dynamical Systems


  • Author : Michael Shub
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-04-17
  • Genre: Mathematics
  • Pages : 150
  • ISBN 10 : 9781475719475

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Global Stability of Dynamical Systems Excerpt :

These notes are the result of a course in dynamical systems given at Orsay during the 1976-77 academic year. I had given a similar course at the Gradu ate Center of the City University of New York the previous year and came to France equipped with the class notes of two of my students there, Carol Hurwitz and Michael Maller. My goal was to present Smale's n-Stability Theorem as completely and compactly as possible and in such a way that the students would have easy access to the literature. I was not confident that I could do all this in lectures in French, so I decided to distribute lecture notes. I wrote these notes in English and Remi Langevin translated them into French. His work involved much more than translation. He consistently corrected for style, clarity, and accuracy. Albert Fathi got involved in reading the manuscript. His role quickly expanded to extensive rewriting and writing. Fathi wrote (5. 1) and (5. 2) and rewrote Theorem 7. 8 when I was in despair of ever getting it right with all the details. He kept me honest at all points and played a large role in the final form of the manuscript. He also did the main work in getting the manuscript ready when I had left France and Langevin was unfortunately unavailable. I ran out of steam by the time it came to Chapter 10. M.

Stability Theory of Dynamical Systems Book

Stability Theory of Dynamical Systems


  • Author : N.P. Bhatia
  • Publisher : Springer Science & Business Media
  • Release Date : 2002-01-10
  • Genre: Science
  • Pages : 225
  • ISBN 10 : 3540427481

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Stability Theory of Dynamical Systems Excerpt :

Reprint of classic reference work. Over 400 books have been published in the series Classics in Mathematics, many remain standard references for their subject. All books in this series are reissued in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. "... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well-written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."

Dynamical Systems Book

Dynamical Systems


  • Author : Anonim
  • Publisher : CRC Press
  • Release Date : 1998-11-17
  • Genre: Mathematics
  • Pages : 520
  • ISBN 10 : 9781482227871

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Dynamical Systems Excerpt :

Several distinctive aspects make Dynamical Systems unique, including: treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas through examples and at a level accessible to a beginning graduate student

Stability and Control of Large Scale Dynamical Systems Book

Stability and Control of Large Scale Dynamical Systems


  • Author : Wassim M. Haddad
  • Publisher : Princeton University Press
  • Release Date : 2011-12-04
  • Genre: Mathematics
  • Pages : 371
  • ISBN 10 : 9780691153469

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Stability and Control of Large Scale Dynamical Systems Excerpt :

Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of technological, environmental, and social phenomena. This book develops stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems.

Bifurcation and Stability in Nonlinear Dynamical Systems Book

Bifurcation and Stability in Nonlinear Dynamical Systems


  • Author : Albert C. J. Luo
  • Publisher : Springer Nature
  • Release Date : 2020-01-30
  • Genre: Mathematics
  • Pages : 411
  • ISBN 10 : 9783030229108

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Bifurcation and Stability in Nonlinear Dynamical Systems Excerpt :

This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems. Until now, one does not have any efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums. For instance, infinite-equilibrium dynamical systems have higher-order singularity, which dramatically changes dynamical behaviors and possesses the similar characteristics of discontinuous dynamical systems. The stability and bifurcation of equilibriums on the specific eigenvector are presented, and the spiral stability and Hopf bifurcation of equilibriums in nonlinear systems are presented through the Fourier series transformation. The bifurcation and stability of higher-order singularity equilibriums are presented through the (2m)th and (2m+1)th -degree polynomial systems. From local analysis, dynamics of infinite-equilibrium systems is discussed. The research on infinite-equilibrium systems will bring us to the new era of dynamical systems and control. Presents an efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums; Discusses dynamics of infinite-equilibrium systems; Demonstrates higher-order singularity.

Stability Theory of Switched Dynamical Systems Book

Stability Theory of Switched Dynamical Systems


  • Author : Zhendong Sun
  • Publisher : Springer Science & Business Media
  • Release Date : 2011-01-06
  • Genre: Technology & Engineering
  • Pages : 256
  • ISBN 10 : 9780857292568

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Stability Theory of Switched Dynamical Systems Excerpt :

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.

Lectures on Dynamical Systems  Structural Stability  and Their Applications Book

Lectures on Dynamical Systems Structural Stability and Their Applications


  • Author : Kotik K. Lee
  • Publisher : World Scientific
  • Release Date : 1992
  • Genre: Science
  • Pages : 454
  • ISBN 10 : 9971509652

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Lectures on Dynamical Systems Structural Stability and Their Applications Excerpt :

The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.

The Stability of Dynamical Systems Book

The Stability of Dynamical Systems


  • Author : J. P. LaSalle
  • Publisher : SIAM
  • Release Date : 1976-01-01
  • Genre: Mathematics
  • Pages : 76
  • ISBN 10 : 9780898710229

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The Stability of Dynamical Systems Excerpt :

An introduction to aspects of the theory of dynamical systems based on extensions of Liapunov's direct method. The main ideas and structure for the theory are presented for difference equations and for the analogous theory for ordinary differential equations and retarded functional differential equations.

Stable and Random Motions in Dynamical Systems Book

Stable and Random Motions in Dynamical Systems


  • Author : Jurgen Moser
  • Publisher : Princeton University Press
  • Release Date : 2016-03-02
  • Genre: Science
  • Pages : 216
  • ISBN 10 : 9781400882694

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Stable and Random Motions in Dynamical Systems Excerpt :

For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.

Hybrid Dynamical Systems Book

Hybrid Dynamical Systems


  • Author : Rafal Goebel
  • Publisher : Princeton University Press
  • Release Date : 2012-03-18
  • Genre: Mathematics
  • Pages : 232
  • ISBN 10 : 9781400842636

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Hybrid Dynamical Systems Excerpt :

Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms. This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.

Uncertain Dynamical Systems Book

Uncertain Dynamical Systems


  • Author : A.A. Martynyuk
  • Publisher : CRC Press
  • Release Date : 2011-11-28
  • Genre: Mathematics
  • Pages : 310
  • ISBN 10 : 9781439876879

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Uncertain Dynamical Systems Excerpt :

This self-contained book provides systematic instructive analysis of uncertain systems of the following types: ordinary differential equations, impulsive equations, equations on time scales, singularly perturbed differential equations, and set differential equations. Each chapter contains new conditions of stability of unperturbed motion of the abo

Stability Regions of Nonlinear Dynamical Systems Book

Stability Regions of Nonlinear Dynamical Systems


  • Author : Hsiao-Dong Chiang
  • Publisher : Cambridge University Press
  • Release Date : 2015-07-31
  • Genre: Mathematics
  • Pages : 450
  • ISBN 10 : 9781107035409

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Stability Regions of Nonlinear Dynamical Systems Excerpt :

An authoritative treatment by leading researchers covering theory and optimal estimation, along with practical applications.