Stability By Liapunovs Direct Method With Application

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Stability by Liapunov's Direct Method with Applications by Joseph L Salle and Solomon Lefschetz

Author :
Publisher : Elsevier
ISBN 13 : 0080955126
Total Pages : 142 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Stability by Liapunov's Direct Method with Applications by Joseph L Salle and Solomon Lefschetz by :

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

Stability Theory by Liapunov’s Direct Method

Author : Nicolas Rouche
Publisher : Springer Science & Business Media
ISBN 13 : 1468493620
Total Pages : 408 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Stability Theory by Liapunov’s Direct Method by : Nicolas Rouche

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].

Liapunov Functions and Stability in Control Theory

Author : Andrea Bacciotti
Publisher : Springer Science & Business Media
ISBN 13 : 9783540213321
Total Pages : 264 pages
Book Rating : 4.2/5 (133 download)

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Book Synopsis Liapunov Functions and Stability in Control Theory by : Andrea Bacciotti

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.

Stability of Dynamical Systems

Author : Xiaoxin Liao
Publisher : Elsevier
ISBN 13 : 0080550614
Total Pages : 719 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Stability of Dynamical Systems by : Xiaoxin Liao

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

Stability by Liapunov's Matrix Function Method with Applications

Author : A.A. Martynyuk
Publisher : CRC Press
ISBN 13 : 9780824701918
Total Pages : 298 pages
Book Rating : 4.7/5 (19 download)

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Book Synopsis Stability by Liapunov's Matrix Function Method with Applications by : A.A. Martynyuk

Download or read book Stability by Liapunov's Matrix Function Method with Applications written by A.A. Martynyuk and published by CRC Press. This book was released on 1998-08-03 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Provides a systematic study of matrix Liapunov functions, incorporating new techniques for the qualitative analysis of nonlinear systems encountered in a wide variety of real-world situations."

Direct Methods for Stability Analysis of Electric Power Systems

Author : Hsiao-Dong Chiang
Publisher : John Wiley & Sons
ISBN 13 : 1118088123
Total Pages : 461 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Direct Methods for Stability Analysis of Electric Power Systems by : Hsiao-Dong Chiang

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.

Nonlinear Differential Equations and Dynamical Systems

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
ISBN 13 : 3642971490
Total Pages : 287 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Nonlinear Differential Equations and Dynamical Systems by : Ferdinand Verhulst

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.

Optimization Methods and Applications

Author : Xiao-qi Yang
Publisher : Springer Science & Business Media
ISBN 13 : 147573333X
Total Pages : 439 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Optimization Methods and Applications by : Xiao-qi Yang

Download or read book Optimization Methods and Applications written by Xiao-qi Yang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book is dedicated to Professor N. U. Ahmed, a leading scholar and a renowned researcher in optimal control and optimization on the occasion of his retirement from the Department of Electrical Engineering at University of Ottawa in 1999. The contributions of this volume are in the areas of optimal control, non linear optimization and optimization applications. They are mainly the im proved and expanded versions of the papers selected from those presented in two special sessions of two international conferences. The first special session is Optimization Methods, which was organized by K. L. Teo and X. Q. Yang for the International Conference on Optimization and Variational Inequality, the City University of Hong Kong, Hong Kong, 1998. The other one is Optimal Control, which was organized byK. ~Teo and L. Caccetta for the Dynamic Control Congress, Ottawa, 1999. This volume is divided into three parts: Optimal Control; Optimization Methods; and Applications. The Optimal Control part is concerned with com putational methods, modeling and nonlinear systems. Three computational methods for solving optimal control problems are presented: (i) a regularization method for computing ill-conditioned optimal control problems, (ii) penalty function methods that appropriately handle final state equality constraints, and (iii) a multilevel optimization approach for the numerical solution of opti mal control problems. In the fourth paper, the worst-case optimal regulation involving linear time varying systems is formulated as a minimax optimal con trol problem.

Applied Mathematical Analysis: Theory, Methods, and Applications

Author : Hemen Dutta
Publisher : Springer
ISBN 13 : 3319999184
Total Pages : 809 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Applied Mathematical Analysis: Theory, Methods, and Applications by : Hemen Dutta

Download or read book Applied Mathematical Analysis: Theory, Methods, and Applications written by Hemen Dutta and published by Springer. This book was released on 2019-02-21 with total page 809 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses key aspects of recent developments in applied mathematical analysis and its use. It also highlights a broad range of applications from science, engineering, technology and social perspectives. Each chapter investigates selected research problems and presents a balanced mix of theory, methods and applications for the chosen topics. Special emphasis is placed on presenting basic developments in applied mathematical analysis, and on highlighting the latest advances in this research area. The book is presented in a self-contained manner as far as possible, and includes sufficient references to allow the interested reader to pursue further research in this still-developing field. The primary audience for this book includes graduate students, researchers and educators; however, it will also be useful for general readers with an interest in recent developments in applied mathematical analysis and applications.

Transient Stability of Power Systems

Author : Mania Pavella
Publisher : Springer Science & Business Media
ISBN 13 : 1461543193
Total Pages : 251 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Transient Stability of Power Systems by : Mania Pavella

Download or read book Transient Stability of Power Systems written by Mania Pavella and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The market liberalization is expected to affect drastically the operation of power systems, which under economical pressure and increasing amount of transactions are being operated much closer to their limits than previously. These changes put the system operators faced with rather different and much more problematic scenarios than in the past. They have now to calculate available transfer capabilities and manage congestion problems in a near on line environment, while operating the transmission system under extremely stressed conditions. This requires highly reliable and efficient software aids, which today are non-existent, or not yet in use. One of the most problematic issues, very much needed but not yet en countered today, is on-line dynamic security assessment and control, enabling the power system to withstand unexpected contingencies without experienc ing voltage or transient instabilities. This monograph is devoted to a unified approach to transient stability assessment and control, called SIngle Machine Equivalent (S1ME).

State Estimation and Stabilization of Nonlinear Systems

Author : Abdellatif Ben Makhlouf
Publisher : Springer Nature
ISBN 13 : 3031379705
Total Pages : 439 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis State Estimation and Stabilization of Nonlinear Systems by : Abdellatif Ben Makhlouf

Download or read book State Estimation and Stabilization of Nonlinear Systems written by Abdellatif Ben Makhlouf and published by Springer Nature. This book was released on 2023-11-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the separation principle which is also known as the principle of separation of estimation and control and states that, under certain assumptions, the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the system's state, which feeds into an optimal deterministic controller for the system. Thus, the problem may be divided into two halves, which simplifies its design. In the context of deterministic linear systems, the first instance of this principle is that if a stable observer and stable state feedback are built for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback are stable. The separation principle does not true for nonlinear systems in general. Another instance of the separation principle occurs in the context of linear stochastic systems, namely that an optimum state feedback controller intended to minimize a quadratic cost is optimal for the stochastic control problem with output measurements. The ideal solution consists of a Kalman filter and a linear-quadratic regulator when both process and observation noise are Gaussian. The term for this is linear-quadratic-Gaussian control. More generally, given acceptable conditions and when the noise is a martingale (with potential leaps), a separation principle, also known as the separation principle in stochastic control, applies when the noise is a martingale (with possible jumps).

PDE Modeling and Boundary Control for Flexible Mechanical System

Author : Zhijie Liu
Publisher : Springer Nature
ISBN 13 : 981152596X
Total Pages : 184 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis PDE Modeling and Boundary Control for Flexible Mechanical System by : Zhijie Liu

Download or read book PDE Modeling and Boundary Control for Flexible Mechanical System written by Zhijie Liu and published by Springer Nature. This book was released on 2020-03-16 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive review of fundamental issues in the dynamical modeling and vibration control design for several flexible mechanical systems, such as flexible satellites, flexible aerial refueling hoses, and flexible three-dimensional manipulators. Offering an authoritative reference guide to the dynamics and control of flexible mechanical systems, it equips readers to solve a host of problems concerning these systems. It provides not only a complete overview of flexible systems, but also a better understanding of the technical levels involved. The book is divided into ten chapters: Chapters 1 and 2 lay the foundations, while the remaining chapters explore several independent yet related topics in detail. The book’s final chapter presents conclusions and recommendations for future research. Given its scope, the book is intended for researchers, graduate students, and engineers whose work involves control systems, flexible mechanical systems, and related areas.

Chaos Theory: Modeling, Simulation And Applications - Selected Papers From The 3rd Chaotic Modeling And Simulation International Conference (Chaos2010)

Download Chaos Theory: Modeling, Simulation And Applications - Selected Papers From The 3rd Chaotic Modeling And Simulation International Conference (Chaos2010) PDF Online Free

Author : Christos H Skiadas
Publisher : World Scientific
ISBN 13 : 9814460478
Total Pages : 467 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Chaos Theory: Modeling, Simulation And Applications - Selected Papers From The 3rd Chaotic Modeling And Simulation International Conference (Chaos2010) by : Christos H Skiadas

Download or read book Chaos Theory: Modeling, Simulation And Applications - Selected Papers From The 3rd Chaotic Modeling And Simulation International Conference (Chaos2010) written by Christos H Skiadas and published by World Scientific. This book was released on 2011-05-31 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work done in chaotic modeling and simulation during the last decades has changed our views of the world around us and has introduced new scientific tools, methods and techniques. Advanced topics of these achievements are included in this volume on Chaos Theory which focuses on Chaotic Modeling, Simulation and Applications of the nonlinear phenomena. This volume includes the best papers presented in the 3rd International Conference on CHAOS. This interdisciplinary conference attracted people from many scientific fields dealing with chaos, nonlinear dynamics, fractals and the works presented and the papers included here are of particular interest that could provide a broad understanding of chaos in its various forms.The chapters relate to many fields of chaos including Dynamical and Nonlinear Systems, Attractors and Fractals, Hydro-Fluid Dynamics and Mechanics, Chaos in Meteorology and Cosmology, Chaos in Biology and Genetics, Chaotic Control, Chaos in Economy and Markets, and Computer Composition and Chaotic Simulations, including related applications.

Adaptive Control Systems

Author : Chalam
Publisher : Routledge
ISBN 13 : 1351468987
Total Pages : 544 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Adaptive Control Systems by : Chalam

Download or read book Adaptive Control Systems written by Chalam and published by Routledge. This book was released on 2017-10-19 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: impossible to access. It has been widely scattered in papers, reports, and proceedings ofsymposia, with different authors employing different symbols and terms. But now thereis a book that covers all aspects of this dynamic topic in a systematic manner.Featuring consistent terminology and compatible notation, and emphasizing unifiedstrategies, Adaptive Control Systems provides a comprehensive, integrated accountof basic concepts, analytical tools, algorithms, and a wide variety of application trendsand techniques.Adaptive Control Systems deals not only with the two principal approachesmodelreference adaptive control and self-tuning regulators-but also considers otheradaptive strategies involving variable structure systems, reduced order schemes, predictivecontrol, fuzzy logic, and more. In addition, it highlights a large number of practical applicationsin a range of fields from electrical to biomedical and aerospace engineering ...and includes coverage of industrial robots.The book identifies current trends in the development of adaptive control systems ...delineates areas for further research . : . and provides an invaluable bibliography of over1,200 references to the literature.The first authoritative reference in this important area of work, Adaptive ControlSystems is an essential information source for electrical and electronics, R&D,chemical, mechanical, aerospace, biomedical, metallurgical, marine, transportation, andpower plant engineers. It is also useful as a text in professional society seminars and inhousetraining programs for personnel involved with the control of complex systems, andfor graduate students engaged in the study of adaptive control systems.

Chaotic Dynamics

Author : Alfredo Medio
Publisher : Cambridge University Press
ISBN 13 : 9780521484619
Total Pages : 368 pages
Book Rating : 4.4/5 (846 download)

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Book Synopsis Chaotic Dynamics by : Alfredo Medio

Download or read book Chaotic Dynamics written by Alfredo Medio and published by Cambridge University Press. This book was released on 1992 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modelling of economic models by means of dynamic systems.

Proceedings of the Tenth Power Systems Computation Conference

Author : Graz Austria
Publisher : Elsevier
ISBN 13 : 1483101045
Total Pages : 1281 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Proceedings of the Tenth Power Systems Computation Conference by : Graz Austria

Download or read book Proceedings of the Tenth Power Systems Computation Conference written by Graz Austria and published by Elsevier. This book was released on 2016-06-06 with total page 1281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Tenth Power Systems Computation Conference

Frequency-domain Methods For Nonlinear Analysis: Theory And Applications

Author : Gennady A Leonov
Publisher : World Scientific
ISBN 13 : 9814500909
Total Pages : 512 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Frequency-domain Methods For Nonlinear Analysis: Theory And Applications by : Gennady A Leonov

Download or read book Frequency-domain Methods For Nonlinear Analysis: Theory And Applications written by Gennady A Leonov and published by World Scientific. This book was released on 1996-05-09 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the investigation of global attractors of nonlinear dynamical systems. The exposition proceeds from the simplest attractor of a single equilibrium to more complicated ones, i.e. to finite, denumerable and continuum equilibria sets; and further, to cycles, homoclinic and heteroclinic orbits; and finally, to strange attractors consisting of irregular unstable trajectories. On the complicated equilibria sets, the methods of Lyapunov stability theory are transferred. They are combined with stability techniques specially elaborated for such sets. The results are formulated as frequency-domain criteria. The methods connected with the theorems of existence of cycles and homoclinic orbits are developed. The estimates of Hausdorff dimensions of attractors are presented.