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 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 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 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 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 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 Theory for Dynamic Equations on Time Scales written by Anatoly A. Martynyuk and published by Birkhäuser. This book was released on 2016-09-22 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.
Download or read book Generalized Ordinary Differential Equations in Abstract Spaces and Applications written by Everaldo M. Bonotto and published by John Wiley & Sons. This book was released on 2021-09-15 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. Throughout the book, the focus is on qualitative theory and on corresponding results for other types of differential equations, as well as the connection between Generalized Ordinary Differential Equations and impulsive differential equations, functional differential equations, measure differential equations and dynamic equations on time scales. The book’s descriptions will be of use in many mathematical contexts, as well as in the social and natural sciences. Readers will also benefit from the inclusion of: A thorough introduction to regulated functions, including their basic properties, equiregulated sets, uniform convergence, and relatively compact sets An exploration of the Kurzweil integral, including its definitions and basic properties A discussion of measure functional differential equations, including impulsive measure FDEs The interrelationship between generalized ODEs and measure FDEs A treatment of the basic properties of generalized ODEs, including the existence and uniqueness of solutions, and prolongation and maximal solutions Perfect for researchers and graduate students in Differential Equations and Dynamical Systems, Generalized Ordinary Differential Equations in Abstract Spaces and Applications will also earn a place in the libraries of advanced undergraduate students taking courses in the subject and hoping to move onto graduate studies.
Download or read book Random Dynamical Systems written by Ludwig Arnold and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
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 Advances in Stability Theory at the End of the 20th Century written by A.A. Martynyuk and published by CRC Press. This book was released on 2002-10-03 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents surveys and research papers on various aspects of modern stability theory, including discussions on modern applications of the theory, all contributed by experts in the field. The volume consists of four sections that explore the following directions in the development of stability theory: progress in stability theory by first approximation; contemporary developments in Lyapunov's idea of the direct method; the stability of solutions to periodic differential systems; and selected applications. Advances in Stability Theory at the End of the 20th Century will interest postgraduates and researchers in engineering fields as well as those in mathematics.
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 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 Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems written by V. Lakshmikantham and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi, "', si j'avait su comment en revenir, je n'y serais point all".' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . .'; 'One service logic has rendered com puter science . .'; 'One service category theory has rendered mathematics . .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Download or read book A Mathematical Introduction to Robotic Manipulation written by Richard M. Murray and published by CRC Press. This book was released on 2017-12-14 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematical Introduction to Robotic Manipulation presents a mathematical formulation of the kinematics, dynamics, and control of robot manipulators. It uses an elegant set of mathematical tools that emphasizes the geometry of robot motion and allows a large class of robotic manipulation problems to be analyzed within a unified framework. The foundation of the book is a derivation of robot kinematics using the product of the exponentials formula. The authors explore the kinematics of open-chain manipulators and multifingered robot hands, present an analysis of the dynamics and control of robot systems, discuss the specification and control of internal forces and internal motions, and address the implications of the nonholonomic nature of rolling contact are addressed, as well. The wealth of information, numerous examples, and exercises make A Mathematical Introduction to Robotic Manipulation valuable as both a reference for robotics researchers and a text for students in advanced robotics courses.
