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Author: Vangipuram Lakshmikantham
Publisher: Birkhäuser
ISBN: 3319272004
Category : Mathematics
Languages : en
Pages : 339
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Book Description
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: Vangipuram Lakshmikantham
Publisher: Birkhäuser
ISBN: 3319272004
Category : Mathematics
Languages : en
Pages : 339
Get Book Here
Book Description
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: Iasson Karafyllis
Publisher: Springer Science & Business Media
ISBN: 0857295136
Category : Technology & Engineering
Languages : en
Pages : 401
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Book Description
Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of their stability and feedback stabilization which enables the reader to learn and understand major techniques used in mathematical control theory. In particular: the important techniques of proving global stability properties are presented closely linked with corresponding methods of nonlinear feedback stabilization; a general framework of methods for proving stability is given, thus allowing the study of a wide class of nonlinear systems, including finite-dimensional systems described by ordinary differential equations, discrete-time systems, systems with delays and sampled-data systems; approaches to the proof of classical global stability properties are extended to non-classical global stability properties such as non-uniform-in-time stability and input-to-output stability; and new tools for stability analysis and control design of a wide class of nonlinear systems are introduced. The presentational emphasis of Stability and Stabilization of Nonlinear Systems is theoretical but the theory’s importance for concrete control problems is highlighted with a chapter specifically dedicated to applications and with numerous illustrative examples. Researchers working on nonlinear control theory will find this monograph of interest while graduate students of systems and control can also gain much insight and assistance from the methods and proofs detailed in this book.
Author: Seyed Kamaleddin Yadavar Nikravesh
Publisher: CRC Press
ISBN: 1466569298
Category : Science
Languages : en
Pages : 319
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Book Description
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: Xiao-Xin Liao
Publisher: Springer Science & Business Media
ISBN: 9401706085
Category : Science
Languages : en
Pages : 186
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Book Description
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: V. Lakshmikantham
Publisher: World Scientific
ISBN: 9789810203566
Category : Computers
Languages : en
Pages : 228
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Book Description
This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.
Author: V. Lakshmikantham
Publisher: Springer Science & Business Media
ISBN: 9401579393
Category : Mathematics
Languages : en
Pages : 182
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Book Description
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.
Author: Shankar Sastry
Publisher: Springer Science & Business Media
ISBN: 1475731086
Category : Mathematics
Languages : en
Pages : 690
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Book Description
There has been much excitement over the emergence of new mathematical techniques for the analysis and control of nonlinear systems. In addition, great technological advances have bolstered the impact of analytic advances and produced many new problems and applications which are nonlinear in an essential way. This book lays out in a concise mathematical framework the tools and methods of analysis which underlie this diversity of applications.
Author: Albert C. J. Luo
Publisher: Springer Nature
ISBN: 3030229106
Category : Mathematics
Languages : en
Pages : 418
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Book Description
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: Sophie Tarbouriech
Publisher: Springer Science & Business Media
ISBN: 0857299417
Category : Technology & Engineering
Languages : en
Pages : 441
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Book Description
This monograph details basic concepts and tools fundamental for the analysis and synthesis of linear systems subject to actuator saturation and developments in recent research. The authors use a state-space approach and focus on stability analysis and the synthesis of stabilizing control laws in both local and global contexts. Different methods of modeling the saturation and behavior of the nonlinear closed-loop system are given special attention. Various kinds of Lyapunov functions are considered to present different stability conditions. Results arising from uncertain systems and treating performance in the presence of saturation are given. The text proposes methods and algorithms, based on the use of linear programming and linear matrix inequalities, for computing estimates of the basin of attraction and for designing control systems accounting for the control bounds and the possibility of saturation. They can be easily implemented with mathematical software packages.
Author: Anatoly Martynyuk
Publisher: CRC Press
ISBN: 1466570865
Category : Mathematics
Languages : en
Pages : 230
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Book Description
Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected equations. After supplying the necessary mathematical foundation, the book illustrates recent approaches to studying the boundedness of motion of weakly connected nonlinear systems. The authors consider conditions for asymptotic and uniform stability using the auxiliary vector Lyapunov functions and explore the polystability of the motion of a nonlinear system with a small parameter. Using the generalization of the direct Lyapunov method with the asymptotic method of nonlinear mechanics, they then study the stability of solutions for nonlinear systems with small perturbing forces. They also present fundamental results on the boundedness and stability of systems in Banach spaces with weakly connected subsystems through the generalization of the direct Lyapunov method, using both vector and matrix-valued auxiliary functions. Designed for researchers and graduate students working on systems with a small parameter, this book will help readers get up to date on the knowledge required to start research in this area.
