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Author : Charles Joseph Monier
Publisher :
ISBN 13 :
Total Pages : 123 pages
Book Rating : 4.:/5 (224 download)
Download or read book Stability Investigation of Certain Nonlinear Autonomous Systems written by Charles Joseph Monier and published by . This book was released on 1966 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : K. C. Cowan
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (428 download)
Download or read book Stability Analysis of Nonlinear Autonomous Systems by Numerical Methods written by K. C. Cowan and published by . This book was released on 1967 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vangipuram Lakshmikantham
Publisher : Birkhäuser
ISBN 13 : 3319272004
Total Pages : 339 pages
Book Rating : 4.3/5 (192 download)
Download or read book Stability Analysis of Nonlinear Systems written by Vangipuram Lakshmikantham and published by Birkhäuser. This book was released on 2015-12-29 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Author : V. V. Kazakevich
Publisher :
ISBN 13 :
Total Pages : 62 pages
Book Rating : 4.:/5 (227 download)
Download or read book Approximate Investigation of Some Types of Strongly Nonlinear Autonomous Systems written by V. V. Kazakevich and published by . This book was released on 1963 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Seyed Kamaleddin Yadavar Nikravesh
Publisher : CRC Press
ISBN 13 : 1466569298
Total Pages : 319 pages
Book Rating : 4.4/5 (665 download)
Download or read book Nonlinear Systems Stability Analysis written by Seyed Kamaleddin Yadavar Nikravesh and published by CRC Press. This book was released on 2018-09-03 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equations used to describe dynamic properties of physical systems are often nonlinear, and it is rarely possible to find their solutions. Although numerical solutions are impractical and graphical techniques are not useful for many types of systems, there are different theorems and methods that are useful regarding qualitative properties of nonlinear systems and their solutions—system stability being the most crucial property. Without stability, a system will not have value. Nonlinear Systems Stability Analysis: Lyapunov-Based Approach introduces advanced tools for stability analysis of nonlinear systems. It presents the most recent progress in stability analysis and provides a complete review of the dynamic systems stability analysis methods using Lyapunov approaches. The author discusses standard stability techniques, highlighting their shortcomings, and also describes recent developments in stability analysis that can improve applicability of the standard methods. The text covers mostly new topics such as stability of homogonous nonlinear systems and higher order Lyapunov functions derivatives for stability analysis. It also addresses special classes of nonlinear systems including time-delayed and fuzzy systems. Presenting new methods, this book provides a nearly complete set of methods for constructing Lyapunov functions in both autonomous and nonautonomous systems, touching on new topics that open up novel research possibilities. Gathering a body of research into one volume, this text offers information to help engineers design stable systems using practice-oriented methods and can be used for graduate courses in a range of engineering disciplines.
Author : M. Vidyasagar
Publisher : SIAM
ISBN 13 : 9780898719185
Total Pages : 515 pages
Book Rating : 4.7/5 (191 download)
Download or read book Nonlinear Systems Analysis written by M. Vidyasagar and published by SIAM. This book was released on 2002-01-01 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.
Author : Seyed Kamaleddin Yadavar Nikravesh
Publisher : CRC Press
ISBN 13 : 1351831887
Total Pages : 323 pages
Book Rating : 4.3/5 (518 download)
Download or read book Nonlinear Systems Stability Analysis written by Seyed Kamaleddin Yadavar Nikravesh and published by CRC Press. This book was released on 2018-09-03 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equations used to describe dynamic properties of physical systems are often nonlinear, and it is rarely possible to find their solutions. Although numerical solutions are impractical and graphical techniques are not useful for many types of systems, there are different theorems and methods that are useful regarding qualitative properties of nonlinear systems and their solutions—system stability being the most crucial property. Without stability, a system will not have value. Nonlinear Systems Stability Analysis: Lyapunov-Based Approach introduces advanced tools for stability analysis of nonlinear systems. It presents the most recent progress in stability analysis and provides a complete review of the dynamic systems stability analysis methods using Lyapunov approaches. The author discusses standard stability techniques, highlighting their shortcomings, and also describes recent developments in stability analysis that can improve applicability of the standard methods. The text covers mostly new topics such as stability of homogonous nonlinear systems and higher order Lyapunov functions derivatives for stability analysis. It also addresses special classes of nonlinear systems including time-delayed and fuzzy systems. Presenting new methods, this book provides a nearly complete set of methods for constructing Lyapunov functions in both autonomous and nonautonomous systems, touching on new topics that open up novel research possibilities. Gathering a body of research into one volume, this text offers information to help engineers design stable systems using practice-oriented methods and can be used for graduate courses in a range of engineering disciplines.
Author : Anhtuan Nguyen Duy
Publisher :
ISBN 13 :
Total Pages : 300 pages
Book Rating : 4.:/5 (365 download)
Download or read book Transient Stability Analysis of Stability Regions for Nonlinear Autonomous Systems Via Direct Methods and Its Application in Power Systems written by Anhtuan Nguyen Duy and published by . This book was released on 1996 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ratnadip Adhikari
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659342196
Total Pages : 84 pages
Book Rating : 4.3/5 (421 download)
Download or read book A Treatise on Stability of Autonomous and Non-autonomous Systems written by Ratnadip Adhikari and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a stable dynamical system, we broadly mean the one whose overall behavior does not substantially change when its initial conditions or inputs undergo small disturbances. Stability is the fundamental requirement of any practically useful system. The behavior of an unstable system cannot be controlled and hence such a system is simply useless for practical purpose. The aim of this book is to present a concise study of the stability theories of autonomous (time-invariant) and non-autonomous (time-varying) systems. Various related notions and terminologies are meticulously explained. A major focus of the book is on the celebrated Liapunov's direct method which is so far the best mathematical technique for determining the stability nature of a dynamical system. The book introduces and lucidly discusses about the theory of stability of non-autonomous systems which is a complicated subject, having various pitfalls and peculiarities. All concepts in the book are accompanied with illustrative mathematical examples, selected from standard books and journals.
Author : Francesco Amato
Publisher : John Wiley & Sons
ISBN 13 : 1119140528
Total Pages : 184 pages
Book Rating : 4.1/5 (191 download)
Download or read book Finite-Time Stability: An Input-Output Approach written by Francesco Amato and published by John Wiley & Sons. This book was released on 2018-10-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H∞ control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.
Author : A.N. Kounadis
Publisher : Springer
ISBN 13 : 3709143462
Total Pages : 418 pages
Book Rating : 4.7/5 (91 download)
Download or read book Nonlinear Stability of Structures written by A.N. Kounadis and published by Springer. This book was released on 2014-05-04 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume gives a very modern treatment of all theoretical as well as computational aspects of nonlinear structural stability. The theoretical part starts with the basic concepts of nonlinear static stability and classical dynamics and proceeds subsequently with recent progress in nonlinear dynamic stability and dynamic buckling of structures including an introduction to chaos. The first paper overviews theory and modelling of various structural instability problems. In the second section, nonlinear dynamic buckling and stability of autonomous discrete dissipative structural systems, gradient and non-gradient are discussed. The third paper handles stability and bifurcation phenomena in dynamical systems. The fourth paper contains an introduction to nonlinear dynamics and chaos. Special attention is devoted to the direct computation of critical points and path-switching strategies. A variety of numerical simulations for complicated nonlinear unstable responses also illustrate this part.
Author : Guanrong Chen
Publisher : World Scientific
ISBN 13 : 9811279004
Total Pages : 234 pages
Book Rating : 4.8/5 (112 download)
Download or read book Nonlinear Systems: Stability, Dynamics And Control written by Guanrong Chen and published by World Scientific. This book was released on 2023-06-28 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of nonlinear systems is fundamental to the study of systems engineering. So extensive investigations have been carried out by both the nonlinear control and nonlinear dynamics communities, but the focus can be different — on controllers design and dynamics analysis, respectively. The last two decades have witnessed the gradual merging of control theory and dynamics analysis, but not yet to the extent of controlling nonlinear dynamics such as bifurcations and chaos. This monograph is an attempt to fill that gap while presenting a rather comprehensive coverage of the fundamental nonlinear systems theory in a self-contained and approachable manner.This introductory treatise is written for self-study and, in particular, as an elementary textbook that can be taught in a one-semester course to advanced undergraduates or entrance level graduates with curricula focusing on nonlinear systems, both on control theory and dynamics analysis.
Author : Luigi Grippo
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (955 download)
Download or read book A New Approach to the Stability Analysis of Non-linear Discrete-time Autonomous Systems written by Luigi Grippo and published by . This book was released on 1973 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Xiao-Xin Liao
Publisher : Springer Science & Business Media
ISBN 13 : 9401706085
Total Pages : 186 pages
Book Rating : 4.4/5 (17 download)
Download or read book Absolute Stability of Nonlinear Control Systems written by Xiao-Xin Liao and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well-known, a control system always works under a variety of accidental or continued disturbances. Therefore, in designing and analysing the control system, stability is the first thing to be considered. Classic control theory was basically limited to a discussion of linear systems with constant coefficients. The fundamental tools for such studies were the Routh-Hurwitz algebraic criterion and the Nyquist geometric criterion. However, modern control theory mainly deals with nonlinear problems. The stability analysis of nonlinear control systems based on Liapunov stability theory can be traced back to the Russian school of stability. In 1944, the Russian mathematician Lurie, a specialist in control theory, discussed the stability of an autopilot. The well-known Lurie problem and the concept of absolute stability are presented, which is of universal significance both in theory and practice. Up until the end of the 1950's, the field of absolute stability was monopolized mainly by Russian scholars such as A. 1. Lurie, M. A. Aizeman, A. M. Letov and others. At the beginning of the 1960's, some famous American mathematicians such as J. P. LaSalle, S. Lefschetz and R. E. Kalman engaged themself in this field. Meanwhile, the Romanian scholar Popov presented a well-known frequency criterion and consequently ma de a decisive breakthrough in the study of absolute stability.
Author : Albert C. J. Luo
Publisher : Springer Nature
ISBN 13 : 3030229106
Total Pages : 418 pages
Book Rating : 4.0/5 (32 download)
Download or read book Bifurcation and Stability in Nonlinear Dynamical Systems written by Albert C. J. Luo and published by Springer Nature. This book was released on 2020-01-30 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems. Until now, one does not have any efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums. For instance, infinite-equilibrium dynamical systems have higher-order singularity, which dramatically changes dynamical behaviors and possesses the similar characteristics of discontinuous dynamical systems. The stability and bifurcation of equilibriums on the specific eigenvector are presented, and the spiral stability and Hopf bifurcation of equilibriums in nonlinear systems are presented through the Fourier series transformation. The bifurcation and stability of higher-order singularity equilibriums are presented through the (2m)th and (2m+1)th -degree polynomial systems. From local analysis, dynamics of infinite-equilibrium systems is discussed. The research on infinite-equilibrium systems will bring us to the new era of dynamical systems and control. Presents an efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums; Discusses dynamics of infinite-equilibrium systems; Demonstrates higher-order singularity.
Author : Oded Galor
Publisher : Springer Science & Business Media
ISBN 13 : 3540367764
Total Pages : 159 pages
Book Rating : 4.5/5 (43 download)
Download or read book Discrete Dynamical Systems written by Oded Galor and published by Springer Science & Business Media. This book was released on 2007-05-17 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to discrete dynamical systems – a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for those systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors that govern the evolution of state variables in the elementary context of one-dimensional, ?rst-order, linear, autonomous systems. The f- damental insights about the forces that a?ect the evolution of these - ementary systems are subsequently generalized, and the determinants of the trajectories of multi-dimensional, nonlinear, higher-order, non- 1 autonomous dynamical systems are established. Chapter 1 focuses on the analysis of the evolution of state variables in one-dimensional, ?rst-order, autonomous systems. It introduces a method of solution for these systems, and it characterizes the traj- tory of a state variable, in relation to a steady-state equilibrium of the system, examining the local and global (asymptotic) stability of this steady-state equilibrium. The ?rst part of the chapter characterizes the factors that determine the existence, uniqueness and stability of a steady-state equilibrium in the elementary context of one-dimensional, ?rst-order, linear autonomous systems.
Author : Yongduan Song
Publisher : CRC Press
ISBN 13 : 1040098754
Total Pages : 327 pages
Book Rating : 4.0/5 (4 download)
Download or read book Control of Nonlinear Systems written by Yongduan Song and published by CRC Press. This book was released on 2024-08-14 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book Control of Nonlinear Systems–Stability and Performance fills a crucial gap in the field of nonlinear control systems by providing a comprehensive yet accessible treatment of the subject. Unlike many existing texts that are either too complex for beginners or omit essential topics, this book strikes the right balance of mathematical rigor and practicality. The main objective of the book is to simplify and unify the existing techniques for designing and analyzing control systems for nonlinear systems. It aims to alleviate confusion and difficulty in understanding these methods, making it an invaluable resource for students, researchers, and practitioners in the field. By presenting the material in a tutorial manner, the book enhances the reader's understanding of the design and analysis of a wide range of control methods for nonlinear systems. The emphasis on stability and performance highlights the practical relevance of the concepts discussed in the book. Overall, Control of Nonlinear Systems–Stability and Performance is a valuable contribution to the field of nonlinear control systems. Its emphasis on practical applications and its accessible presentation make it an indispensable resource for engineers seeking to enhance their knowledge and skills in this important area of control theory.
