Download or read book Stability Theory by Liapunov s Direct Method written by Nicolas Rouche and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a collective work. The names appear ing on the front cover are those of the people who worked on every chapter. But the contributions of others were also very important: C. Risito for Chapters I, II and IV, K. Peiffer for III, IV, VI, IX R. J. Ballieu for I and IX, Dang Chau Phien for VI and IX, J. L. Corne for VII and VIII. The idea of writing this book originated in a seminar held at the University of Louvain during the academic year 1971-72. Two years later, a first draft was completed. However, it was unsatisfactory mainly because it was ex ce~sively abstract and lacked examples. It was then decided to write it again, taking advantage of -some remarks of the students to whom it had been partly addressed. The actual text is this second version. The subject matter is stability theory in the general setting of ordinary differential equations using what is known as Liapunov's direct or second method. We concentrate our efforts on this method, not because we underrate those which appear more powerful in some circumstances, but because it is important enough, along with its modern developments, to justify the writing of an up-to-date monograph. Also excellent books exist concerning the other methods, as for example R. Bellman [1953] and W. A. Coppel [1965].

Download or read book Stability by Liapunov s Direct Method with Applications by Joseph L Salle and Solomon Lefschetz written by and published by Elsevier. This book was released on 2012-01-25 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, Non-Lagrange interpolation, Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Download or read book Nonlinear Differential Equations and Dynamical Systems written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.

Download or read book Stability of Dynamical Systems written by Xiaoxin Liao and published by Elsevier. This book was released on 2007-08-01 with total page 719 pages. Available in PDF, EPUB and Kindle. Book 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

Download or read book Liapunov Functions and Stability in Control Theory written by Andrea Bacciotti and published by Springer Science & Business Media. This book was released on 2005-04-13 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem of the existence of Liapunov functions (converse Liapunov theorems) and their regularity, whose interest is especially motivated by applications to automatic control. Many recent results in this area have been collected and presented in a systematic way. Some of them are given in extended, unified versions and with new, simpler proofs. In the 2nd edition of this successful book several new sections were added and old sections have been improved, e.g., about the Zubovs method, Liapunov functions for discontinuous systems and cascaded systems. Many new examples, explanations and figures were added making this book accessible and well readable for engineers as well as mathematicians.

Download or read book Direct Methods for Stability Analysis of Electric Power Systems written by Hsiao-Dong Chiang and published by John Wiley & Sons. This book was released on 2011-03-16 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn how to implement BCU methods for fast direct stability assessments of electric power systems Electric power providers around the world rely on stability analysis programs to help ensure uninterrupted service to their customers. These programs are typically based on step-by-step numerical integrations of power system stability models to simulate system dynamic behaviors. Unfortunately, this offline practice is inadequate to deal with current operating environments. For years, direct methods have held the promise of providing real-time stability assessments; however, these methods have presented several challenges and limitations. This book addresses these challenges and limitations with the BCU methods developed by author Hsiao-Dong Chiang. To date, BCU methods have been adopted by twelve major utility companies in Asia and North America. In addition, BCU methods are the only direct methods adopted by the Electric Power Research Institute in its latest version of DIRECT 4.0. Everything you need to take full advantage of BCU methods is provided, including: Theoretical foundations of direct methods Theoretical foundations of energy functions BCU methods and their theoretical foundations Group-based BCU method and its applications Numerical studies on industrial models and data Armed with a solid foundation in the underlying theory of direct methods, energy functions, and BCU methods, you'll discover how to efficiently solve complex practical problems in stability analysis. Most chapters begin with an introduction and end with concluding remarks, making it easy for you to implement these tested and proven methods that will help you avoid costly and dangerous power outages.

Download or read book Control of Nonlinear Dynamical Systems written by Felix L. Chernous'ko and published by Springer Science & Business Media. This book was released on 2008-09-26 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to new methods of control for complex dynamical systems and deals with nonlinear control systems having several degrees of freedom, subjected to unknown disturbances, and containing uncertain parameters. Various constraints are imposed on control inputs and state variables or their combinations. The book contains an introduction to the theory of optimal control and the theory of stability of motion, and also a description of some known methods based on these theories. Major attention is given to new methods of control developed by the authors over the last 15 years. Mechanical and electromechanical systems described by nonlinear Lagrange’s equations are considered. General methods are proposed for an effective construction of the required control, often in an explicit form. The book contains various techniques including the decomposition of nonlinear control systems with many degrees of freedom, piecewise linear feedback control based on Lyapunov’s functions, methods which elaborate and extend the approaches of the conventional control theory, optimal control, differential games, and the theory of stability. The distinctive feature of the methods developed in the book is that the c- trols obtained satisfy the imposed constraints and steer the dynamical system to a prescribed terminal state in ?nite time. Explicit upper estimates for the time of the process are given. In all cases, the control algorithms and the estimates obtained are strictly proven.

Download or read book Nonlinear Dynamical Systems and Control written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2011-09-19 with total page 975 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.

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.

Download or read book Nonlinear Control Systems written by Zoran Vukic and published by CRC Press. This book was released on 2003-02-04 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text emphasizes classical methods and presents essential analytical tools and strategies for the construction and development of improved design methods in nonlinear control. It offers engineering procedures for the frequency domain, as well as solved examples for clear understanding of control applications in the industrial, electrical, process, manufacturing, and automotive industries. The authors discuss Properties of nonlinear systems, stability, linearization methods, operating modes and dynamic analysis methods, phase trajectories in dynamic analysis of nonlinear systems, and harmonic linearization in dynamic analysis of nonlinear control systems operating in stabilization mode.

Download or read book The Control Handbook written by William S. Levine and published by CRC Press. This book was released on 1996-02-23 with total page 1580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the biggest, most comprehensive, and most prestigious compilation of articles on control systems imaginable. Every aspect of control is expertly covered, from the mathematical foundations to applications in robot and manipulator control. Never before has such a massive amount of authoritative, detailed, accurate, and well-organized information been available in a single volume. Absolutely everyone working in any aspect of systems and controls must have this book!

Download or read book Applied Nonlinear Control written by Jean-Jacques E. Slotine and published by . This book was released on 1991 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the authors present a global perspective on the methods available for analysis and design of non-linear control systems and detail specific applications. They provide a tutorial exposition of the major non-linear systems analysis techniques followed by a discussion of available non-linear design methods.

Download or read book General Problem of the Stability Of Motion written by A M Lyapunov and published by CRC Press. This book was released on 1992-08-28 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book makes more widely accessible the text of Lyapunov's major memoir of the general problem of the stability of motion. Translated by A. T. Fuller (University of Cambridge), the work is now available for the first time in the English language, and marked the centenary of the Russian publication in the late 1800s. Including a biography of Lyapunov and a comprehensive bibliography of his work, this excellent volume will prove to be of fundamental interest to all those concerned with the concept of the stability of motion, boundaries of stability, and with nonlinear dynamics.

Download or read book Power System Stability and Control written by Leonard L. Grigsby and published by CRC Press. This book was released on 2017-12-19 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions from worldwide leaders in the field, Power System Stability and Control, Third Edition (part of the five-volume set, The Electric Power Engineering Handbook) updates coverage of recent developments and rapid technological growth in essential aspects of power systems. Edited by L.L. Grigsby, a respected and accomplished authority in power engineering, and section editors Miroslav Begovic, Prabha Kundur, and Bruce Wollenberg, this reference presents substantially new and revised content. Topics covered include: Power System Protection Power System Dynamics and Stability Power System Operation and Control This book provides a simplified overview of advances in international standards, practices, and technologies, such as small signal stability and power system oscillations, power system stability controls, and dynamic modeling of power systems. This resource will help readers achieve safe, economical, high-quality power delivery in a dynamic and demanding environment. With five new and 10 fully revised chapters, the book supplies a high level of detail and, more importantly, a tutorial style of writing and use of photographs and graphics to help the reader understand the material. New Chapters Cover: Systems Aspects of Large Blackouts Wide-Area Monitoring and Situational Awareness Assessment of Power System Stability and Dynamic Security Performance Wind Power Integration in Power Systems FACTS Devices A volume in the Electric Power Engineering Handbook, Third Edition. Other volumes in the set: K12642 Electric Power Generation, Transmission, and Distribution, Third Edition (ISBN: 9781439856284) K12648 Power Systems, Third Edition (ISBN: 9781439856338) K12650 Electric Power Substations Engineering, Third Edition (9781439856383) K12643 Electric Power Transformer Engineering, Third Edition (9781439856291)

Download or read book Numerical Methods for Linear Control Systems written by Biswa Datta and published by Elsevier. This book was released on 2004-02-24 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. - Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions - Background material in linear algebra, numerical linear algebra, and control theory included in text - Step-by-step explanations of the algorithms and examples

Download or read book Essentials of Nonlinear Control Theory written by James R. Leigh and published by IET. This book was released on 1983 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following topics are dealt with: nonlinearity: dynamic systems; describing function method; phase plane portrait; linearisation ;nonlinear second-order system linearisation; envelope methods; Limit cycles; relaxation oscillations; Lienard's equation; gradient systems and system decomposition.

Download or read book Stability in Nonlinear Control Systems written by Aleksandr Mikhailovich Letov and published by Princeton University Press. This book was released on 2015-12-08 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author, a Nobel prize-winner, has added to the American translation several chapters not in the original. Originally published in 1961. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.