Instability Of Continuous Systems

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Instability of Continuous Systems

Author : Horst Leipholz
Publisher : Springer Science & Business Media
ISBN 13 : 3642650732
Total Pages : 435 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Instability of Continuous Systems by : Horst Leipholz

Download or read book Instability of Continuous Systems written by Horst Leipholz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently there was no uniform stability theory. Different approaches to stability problems had been developed in the different branches of mechanics. In the field of elasticity, it was mainly the so called static method and energy method which were used, while in the field of dynamics it was the kinetic method, which found its perfect expression in the theory of Liapunov. During the last few decades there has been a rapid development in the general theory of stability, stimulated, for example, by the investigations of H. ZIEGLER on elastic systems subject to non-conservative loads, and by the problems arising in aeroelasticity which are closely related to those introduced by ZIEGLER. The need was felt for kinetic methods which could also be used in investigating the stability of deformable systems. Efforts were made to adapt such methods, already known and developed in the stability theory of rigid systems, for application in the stability theory of continuous systems. During the last ten years interest was focused mainly on the application of a generalized Liapunov method to stability problems of continuous systems. All this was done in attempts to unify the various approaches to stability theory. It was with the idea of encouraging such a tendency, establishing to what extent a uniform physical and mathematical foundation already existed for stability theory in all branches of mechanics, and stimulating the further deve lopment of a common stability theory, that a IUTAM-Symposium was devoted to this topic.

Instability of Continuous Systems

Author : Horst Leipholz
Publisher :
ISBN 13 : 9783642650741
Total Pages : 440 pages
Book Rating : 4.6/5 (57 download)

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Book Synopsis Instability of Continuous Systems by : Horst Leipholz

Download or read book Instability of Continuous Systems written by Horst Leipholz and published by . This book was released on 1971 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stability of Dynamical Systems

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0817644865
Total Pages : 516 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Stability of Dynamical Systems by :

Download or read book Stability of Dynamical Systems written by and published by Springer Science & Business Media. This book was released on 2008 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Explicit Stability Conditions for Continuous Systems

Author : Michael I. Gil
Publisher : Springer Science & Business Media
ISBN 13 : 9783540239840
Total Pages : 212 pages
Book Rating : 4.2/5 (398 download)

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Book Synopsis Explicit Stability Conditions for Continuous Systems by : Michael I. Gil

Download or read book Explicit Stability Conditions for Continuous Systems written by Michael I. Gil and published by Springer Science & Business Media. This book was released on 2005-03-17 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explicit Stability Conditions for Continuous Systems deals with non-autonomous linear and nonlinear continuous finite dimensional systems. Explicit conditions for the asymptotic, absolute, input-to-state and orbital stabilities are discussed. This monograph provides new tools for specialists in control system theory and stability theory of ordinary differential equations, with a special emphasis on the Aizerman problem. A systematic exposition of the approach to stability analysis based on estimates for matrix-valued functions is suggested and various classes of systems are investigated from a unified viewpoint.

Theory of Stability of Continuous Elastic Structures

Author : Mario Como
Publisher : Routledge
ISBN 13 : 1351408534
Total Pages : 272 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Theory of Stability of Continuous Elastic Structures by : Mario Como

Download or read book Theory of Stability of Continuous Elastic Structures written by Mario Como and published by Routledge. This book was released on 2022-01-27 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Stability of Continuous Elastic Structures presents an applied mathematical treatment of the stability of civil engineering structures. The book's modern and rigorous approach makes it especially useful as a text in advanced engineering courses and an invaluable reference for engineers.

Explicit Stability Conditions for Continuous Systems

Author : Michael I. Gil
Publisher : Springer
ISBN 13 : 9783540805632
Total Pages : 190 pages
Book Rating : 4.8/5 (56 download)

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Book Synopsis Explicit Stability Conditions for Continuous Systems by : Michael I. Gil

Download or read book Explicit Stability Conditions for Continuous Systems written by Michael I. Gil and published by Springer. This book was released on 2009-09-02 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explicit Stability Conditions for Continuous Systems deals with non-autonomous linear and nonlinear continuous finite dimensional systems. Explicit conditions for the asymptotic, absolute, input-to-state and orbital stabilities are discussed. This monograph provides new tools for specialists in control system theory and stability theory of ordinary differential equations, with a special emphasis on the Aizerman problem. A systematic exposition of the approach to stability analysis based on estimates for matrix-valued functions is suggested and various classes of systems are investigated from a unified viewpoint.

Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems

Author : F.H. Busse
Publisher : Springer Science & Business Media
ISBN 13 : 1468457934
Total Pages : 552 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems by : F.H. Busse

Download or read book Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems written by F.H. Busse and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers contributed to the NATO Advanced Research Workshop "Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems" held in Streitberg, Fed. Rep. Germany, Sept. 24 through 30, 1989. The purpose of the rather long title has been to focus attention on a particularly fruitful direction of research within the broad field covered by terms like Nonlinear Dynamics or Non-Equilibrium Systems. After physicists have been occupied for several decades mainly with the microscopic structure of matter, recent years have witnessed a resurgence of interest in macroscopic patterns and dynamics. Research on these latter phenomena has not been dormant, of course, since fluid dynamicists interested in the origin of turbulence, meteorologists studying weather patterns and numerous other scientists have continued to advance the understanding of the structures relevant to their disciplines. The recent progress in the dynamics of nonl inear systems wi th few degrees of freedom and the discovery of universal laws such as the Feigenbaum scaling of period-doubling cascades has given rise to new hopes for the understanding of common principles underlying the spontaneous formation of structures in extended continuous systems.

Evolution of Spontaneous Structures in Dissipative Continuous Systems

Author : Friedrich H. Busse
Publisher : Springer Science & Business Media
ISBN 13 : 3540495371
Total Pages : 586 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Evolution of Spontaneous Structures in Dissipative Continuous Systems by : Friedrich H. Busse

Download or read book Evolution of Spontaneous Structures in Dissipative Continuous Systems written by Friedrich H. Busse and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the decades the of the formation of structures past subject spontaneous in far from has into a branch of - systems equilibrium major physics grown search with ties to It has become evident that strong neighboring disciplines. a diverse of can be understood within a common mat- phenomena range matical framework which has been called nonlinear of continuous dynamics This name the close to the field of nonlinear systems. emphasizes relationship of with few of freedom which has evolved into a dynamics systems degrees mature in the recent features mathematically subject past. Many dynamical of continuous be described reduction few can a to a systems actually through of freedom and of the latter of continue to degrees properties type systems of continuous the inspire study systems. The of this book is to demonstrate the numerous goal through examples that exist for the of nonlinear the opportunities study phenomena through tools of mathematical and use of common analyses dynamical interpretations. Instead of overview of the a providing comprehensive rapidly evolving field, the contributors to this book are to communicate to a wide scientific trying audience the of what have learnt about the formation of essence they spon- neous structures in continuous and about the dissipative systems competition between order and chaos that characterizes these It is that systems. hoped the book will be even to those scientists whose not helpful are disciplines the authors.

Vibrations of Continuous Systems

Author : Eberhard Brommundt
Publisher : Springer
ISBN 13 : 3709129184
Total Pages : 219 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Vibrations of Continuous Systems by : Eberhard Brommundt

Download or read book Vibrations of Continuous Systems written by Eberhard Brommundt and published by Springer. This book was released on 2014-05-04 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lyapunov Functionals and Stability of Stochastic Difference Equations

Author : Leonid Shaikhet
Publisher : Springer Science & Business Media
ISBN 13 : 085729685X
Total Pages : 374 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Lyapunov Functionals and Stability of Stochastic Difference Equations by : Leonid Shaikhet

Download or read book Lyapunov Functionals and Stability of Stochastic Difference Equations written by Leonid Shaikhet and published by Springer Science & Business Media. This book was released on 2011-06-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is their stability. Stability conditions for difference equations with delay can be obtained using a Lyapunov functional. Lyapunov Functionals and Stability of Stochastic Difference Equations describes a general method of Lyapunov functional construction to investigate the stability of discrete- and continuous-time stochastic Volterra difference equations. The method allows the investigation of the degree to which the stability properties of differential equations are preserved in their difference analogues. The text is self-contained, beginning with basic definitions and the mathematical fundamentals of Lyapunov functional construction and moving on from particular to general stability results for stochastic difference equations with constant coefficients. Results are then discussed for stochastic difference equations of linear, nonlinear, delayed, discrete and continuous types. Examples are drawn from a variety of physical systems including inverted pendulum control, study of epidemic development, Nicholson’s blowflies equation and predator–prey relationships. Lyapunov Functionals and Stability of Stochastic Difference Equations is primarily addressed to experts in stability theory but will also be of use in the work of pure and computational mathematicians and researchers using the ideas of optimal control to study economic, mechanical and biological systems.

Stability Techniques for Continuous Linear Systems

Author : Allan M. Krall
Publisher : CRC Press
ISBN 13 : 9780677014203
Total Pages : 180 pages
Book Rating : 4.0/5 (142 download)

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Book Synopsis Stability Techniques for Continuous Linear Systems by : Allan M. Krall

Download or read book Stability Techniques for Continuous Linear Systems written by Allan M. Krall and published by CRC Press. This book was released on 1967 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Emerging Trends in Vibration and Noise Engineering

Author :
Publisher : Allied Publishers
ISBN 13 : 9788170235323
Total Pages : 468 pages
Book Rating : 4.2/5 (353 download)

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Book Synopsis Emerging Trends in Vibration and Noise Engineering by :

Download or read book Emerging Trends in Vibration and Noise Engineering written by and published by Allied Publishers. This book was released on 1996 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Stability of Dynamical Systems

Author : J. P. LaSalle
Publisher : SIAM
ISBN 13 : 0898710227
Total Pages : 81 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis The Stability of Dynamical Systems by : J. P. LaSalle

Download or read book The Stability of Dynamical Systems written by J. P. LaSalle and published by SIAM. This book was released on 1976-01-01 with total page 81 pages. Available in PDF, EPUB and Kindle. Book 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.

Stability and Stabilization of Time-Delay Systems

Author : Wim Michiels
Publisher : SIAM
ISBN 13 : 0898716322
Total Pages : 383 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Stability and Stabilization of Time-Delay Systems by : Wim Michiels

Download or read book Stability and Stabilization of Time-Delay Systems written by Wim Michiels and published by SIAM. This book was released on 2007-01-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overall solution to the (robust) stability analysis and stabilisation problem of linear time-delay systems.

A Linear Systems Primer

Author : Panos J. Antsaklis
Publisher : Springer Science & Business Media
ISBN 13 : 0817646612
Total Pages : 517 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis A Linear Systems Primer by : Panos J. Antsaklis

Download or read book A Linear Systems Primer written by Panos J. Antsaklis and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a streamlined presentation of the authors’ successful work Linear Systems, this textbook provides an introduction to systems theory with an emphasis on control. Initial chapters present necessary mathematical background material for a fundamental understanding of the dynamical behavior of systems. Each chapter includes helpful chapter descriptions and guidelines for the reader, as well as summaries, notes, references, and exercises at the end. The emphasis throughout is on time-invariant systems, both continuous- and discrete-time.

Advances in Engineering Structures, Mechanics & Construction

Author : M. Pandey
Publisher : Springer Science & Business Media
ISBN 13 : 1402048912
Total Pages : 873 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Advances in Engineering Structures, Mechanics & Construction by : M. Pandey

Download or read book Advances in Engineering Structures, Mechanics & Construction written by M. Pandey and published by Springer Science & Business Media. This book was released on 2007-02-10 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of an International Conference on Advances in Engineering Structures, Mechanics & Construction, held in Waterloo, Ontario, Canada, May 14-17, 2006. The contents include contains the texts of all three plenary presentations and all seventy-three technical papers by more than 153 authors, presenting the latest advances in engineering structures, mechanics and construction research and practice.

Stability and Stabilization of Nonlinear Systems

Author : Iasson Karafyllis
Publisher : Springer Science & Business Media
ISBN 13 : 0857295136
Total Pages : 401 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Stability and Stabilization of Nonlinear Systems by : Iasson Karafyllis

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.