Stability of Dynamical Systems

Stability of Dynamical Systems

Author: Xiaoxin Liao

Publisher: Elsevier

ISBN: 0080550614

Category: Mathematics

Page: 718

View: 879

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

Stability Theory of Dynamical Systems

Stability Theory of Dynamical Systems

Author: N.P. Bhatia

Publisher: Springer Science & Business Media

ISBN: 3540427481

Category: Science

Page: 252

View: 684

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."

Stability of Dynamical Systems

Stability of Dynamical Systems

Author: Anthony N. Michel

Publisher: Springer Science & Business Media

ISBN: 9780817644864

Category: Language Arts & Disciplines

Page: 516

View: 223

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.

The Stability of Dynamical Systems

The Stability of Dynamical Systems

Author: J. P. LaSalle

Publisher: SIAM

ISBN: 1611970431

Category: Difference equations

Page: 81

View: 838

An introduction to aspects of the theory of dynamial 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. The latest results on invariance properties for non-autonomous time-varying systems processes are presented for difference and differential equations.

The Stability of Dynamical Systems

The Stability of Dynamical Systems

Author: J. P. LaSalle

Publisher: Cambridge University Press

ISBN: 0898710227

Category: Mathematics

Page: 90

View: 600

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.

Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs

Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs

Author: Jihoon Lee

Publisher: Springer Nature

ISBN: 9783031120312

Category: Mathematics

Page: 169

View: 993

This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance. In the first part, the authors introduce the notion of Gromov-Hausdorff distance between compact metric spaces, along with the corresponding distance for continuous maps, flows, and group actions on these spaces. They also focus on the stability of certain dynamical objects like shifts, global attractors, and inertial manifolds. Applications to dissipative PDEs, such as the reaction-diffusion and Chafee-Infante equations, are explored in the second part. This text will be of interest to graduates students and researchers working in the areas of topological dynamics and PDEs.

Stability Theory of Switched Dynamical Systems

Stability Theory of Switched Dynamical Systems

Author: Zhendong Sun

Publisher: Springer Science & Business Media

ISBN: 9780857292568

Category: Technology & Engineering

Page: 256

View: 914

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.

Bifurcation and Stability in Nonlinear Dynamical Systems

Bifurcation and Stability in Nonlinear Dynamical Systems

Author: Albert C. J. Luo

Publisher: Springer Nature

ISBN: 9783030229108

Category: Mathematics

Page: 411

View: 214

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.

Lectures on Dynamical Systems, Structural Stability and Their Applications

Lectures on Dynamical Systems, Structural Stability and Their Applications

Author: Kotik K Lee

Publisher: World Scientific

ISBN: 9789814507271

Category: Differentiable dynamical systems

Page: 472

View: 698

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. Contents:IntroductionTopics in Topology and Differential GeometryIntroduction to Global Analysis and Infinite Dimensional ManifoldsGeneral Theory of Dynamical SystemsStability Theory and Liapunov's Direct MethodIntroduction to the General Theory of Structural StabilityApplications Readership: Applied mathematicians and engineers. Keywords:Asymptotically Stable;Bifurcation;Dispersive Systems;Global Analysis;Integral Flow;Liapunov Functions;Linearization;Nonlinear Dynamical Systems;Stable Manifolds;Structural StabilityReview:“The author's style is clear, formulations of mathematical results are precise … The book helps the reader to create a good global picture of the theory of dynamical systems. The author has gathered a considerable number of facts about dynamical systems in this book, including almost 1000 references, so that it can also serve as a handbook for mathematicians beginning to work in this area … The book is useful not only for technicians, but also for mathematicians, and we recommend it to anyone working in dynamical systems.”Alois Klíc Mathematical Reviews