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Author: A.A. Martynyuk
Publisher: CRC Press
ISBN: 9780824701918
Category : Mathematics
Languages : en
Pages : 298
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Book Description
"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."
Author: A.A. Martynyuk
Publisher: CRC Press
ISBN: 9780824701918
Category : Mathematics
Languages : en
Pages : 298
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Book Description
"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."
Author: Zoran Gajic
Publisher: Courier Corporation
ISBN: 048646668X
Category : Mathematics
Languages : en
Pages : 274
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Book Description
This comprehensive treatment provides solutions to many engineering and mathematical problems related to the Lyapunov matrix equation, with self-contained chapters for easy reference. The authors offer a wide variety of techniques for solving and analyzing the algebraic, differential, and difference Lyapunov matrix equations of continuous-time and discrete-time systems. 1995 edition.
Author: Anatoly A. Martynyuk
Publisher: Birkhäuser
ISBN: 3319422138
Category : Mathematics
Languages : en
Pages : 233
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Book Description
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.
Author: A.A. Martynyuk
Publisher: CRC Press
ISBN: 0203166574
Category : Mathematics
Languages : en
Pages : 366
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Book Description
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
Author:
Publisher: Elsevier
ISBN: 0080955126
Category : Mathematics
Languages : en
Pages : 142
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Book Description
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
Author: Vladimir Ivanovich Zubov
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 256
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Book Description
Author: M. A. Pai
Publisher: North-Holland
ISBN:
Category : Electric power system stability
Languages : en
Pages : 276
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Book Description
Author: Junji Kato
Publisher: Routledge
ISBN: 1351414852
Category : Mathematics
Languages : en
Pages : 280
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Book Description
Continuing the strong tradition of functional analysis and stability theory for differential and integral equations already established by the previous volumes in this series, this innovative monograph considers in detail the method of limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed. For the first time, the method first employed by Krylov and Bogolubov in their investigations of oscillations in almost linear systems is applied to a new field: that of the stability problem of systems with small parameters. This important development should facilitate the solution of engineering problems in such areas as orbiting satellites, rocket motion, high-speed vehicles, power grids, and nuclear reactors.
Author: A. Halanay
Publisher: Springer Science & Business Media
ISBN: 9401116008
Category : Science
Languages : en
Pages : 245
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Book Description
The year 1992 marks the centennial anniversary of publication of the celebrated monograph "The General Problem of Stability of Motion" written by A. M. Liapunov. This anniversary inspires to think about the way theory and applications have developed during this century. The first observation one can make is that the so-called "second method", nowadays known as the "Liapunov function method", has received more attention than the "first method"; let us also mention the study of critical cases, which brought more attention recently in connection with the study of bifurcations and with nonlinear stabilization. One of the reasons of popularity of the Liapunov function approach might be the fact that, in many situations in science and engineering, and not only in mechanics, which was the main source of inspiration for the work of Liapunov, natural Liapunov functions may be proposed, intimately connected with the properties of the processes. It is one of the purposes of this book to advocate this idea. From the mathematical viewpoint, the century after the first appear ance of Liapunov's monograph has been characterized both by general izations and by refinements of Liapunov's ideas. But we feel that the most spectacular progress is the understanding of the wide possibilities open for applications by the use of Stability Theory as constructed by Liapunov a century ago. We have tried to show some of the ideas in this direction by start ing with our personal experience in the study of some models.
Author: Wolfgang Hahn
Publisher: Courier Dover Publications
ISBN: 0486839869
Category : Mathematics
Languages : en
Pages : 195
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Book Description
The groundbreaking work of Russian mathematician A. M. Liapunov (1857–1918) on the stability of dynamical systems was overlooked for decades because of political turmoil. During the Cold War, when it was discovered that his method was applicable to the stability of aerospace guidance systems, interest in his research was rekindled. It has remained high ever since. This monograph on both the theory and applications of Liapunov's direct method reflects the work of a period when the theory had been studied seriously for some time and reached a degree of completeness and sophistication. It remains of interest to applied mathematicians in many areas. Topics include applications of the stability theorems to concrete problems, the converse of the main theorems, Liapunov functions with certain properties of rate of change, the sensitivity of the stability behavior to perturbations, the critical cases, and generalizations of the concept of stability.
