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Matrix Methods In Stability Theory

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Matrix Methods In Stability Theory

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Author : Stephen Barnett
language : en
Publisher:
Release Date : 1970

Matrix Methods In Stability Theory written by Stephen Barnett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.

Matrix Methods In Stability Theory

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Author : Stephen Barnett
language : en
Publisher:
Release Date : 1970

Advances In Stability Theory At The End Of The 20th Century

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Author : A.A. Martynyuk
language : en
Publisher: CRC Press
Release Date : 2002-10-03

Advances In Stability Theory At The End Of The 20th Century written by A.A. Martynyuk and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-03 with Mathematics categories.

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

Stability Of Dynamical Systems

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Author : Xiaoxin Liao
language : en
Publisher: Elsevier
Release Date : 2007-08-01

Stability Of Dynamical Systems written by Xiaoxin Liao and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-01 with Mathematics categories.

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 Theory For Dynamic Equations On Time Scales

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Author : Anatoly A. Martynyuk
language : en
Publisher: Birkhäuser
Release Date : 2016-09-22

Stability Theory For Dynamic Equations On Time Scales written by Anatoly A. Martynyuk and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-22 with Mathematics categories.

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.

Stability Theory By Liapunov S Direct Method

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Author : Nicolas Rouche
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Stability Theory By Liapunov S Direct Method written by Nicolas Rouche and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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].

Stability Theory

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Author : Horst Leipholz
language : en
Publisher: Springer
Release Date : 1987-03

Stability Theory written by Horst Leipholz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03 with Science categories.

There have been great advances in theory of stability in recent decades due to the requirements of control theory and flight mechanics, for example. We need only mention the theory of A. M. Lyapunov. A number of specialists have given a very mathematical and abstract description of the Lyapunov stability theory which resulted in a 'stability theory of motion' applicable to the kinetics of rigid bodies and systems. The stability theory of elastomechanics was developed independently. However, there have been a number of important developments in recent years, also with respect to this theory, dealing with the following problems: The concept of the 'follower forces', non-conservative loads, respectively, has been introduced in aeroelasticity. A number of prob lems in elastic kinetics that involve pulsating loads or periodically varying parameters has led to new stability questions. So-called 'kinetic' methods have become necessary in elastomechnics in order to determine the stability bound aries. An evaluation of the stability criteria of elastostatics, which have been assumed to be generally valid, has shown that they can only be applied to a limited number of problems under special assumptions. The transition from stability to instability is a kinetic process in elastomechanics. Therefore, the most general and most certain method of determining stability is the kinetic stability criterion even if in special cases the classical stability criteria of elastostatics may remain valid. This will be discussed in detail in Section 2. 3.

Stability Theory Of Differential Equations

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Author : Richard Bellman
language : en
Publisher: Courier Corporation
Release Date : 2013-02-20

Stability Theory Of Differential Equations written by Richard Bellman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-20 with Mathematics categories.

Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies. The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.

Matrix Methods

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Author : Vadim Olshevsky
language : en
Publisher: World Scientific
Release Date : 2010

Matrix Methods written by Vadim Olshevsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

Operators preserving primitivity for matrix pairs / L.B. Beasley, A.E. Guterman -- Decompositions of quaternions and their matrix equivalents / D. Janovská, G. Opfer -- Sensitivity analysis of Hamiltonian and reversible systems prone to dissipation-induced instabilities / O.N. Kirillov -- Block triangular miniversal deformations of matrices and matrix pencils / L. Klimenko, V.V. Sergeichuk -- Determining the Schein rank of boolean matrices / E.E. Marenich -- Lattices of matrix rows and matrix columns. Lattices of invariant column eigenvectors / V. Marenich -- Matrix algebras and their length / O.V. Markova -- On a new class of singular nonsymmetric matrices with nonnegative integer spectra / T. Nahtman, D. von Rosen -- Reduction of a set of matrices over a principal ideal domain to the Smith normal forms by means of the same one-sided transformation / V.M. Prokip -- Nonsymmetric algebraic Riccati equations associated with an M-matrix : recent advances and algorithms / D.A. Bini, B. Iannazzo, B. Meini, F. Poloni -- A generalized conjugate direction method for nonsymmetric large ill-conditioned linear systems / E.R. Boudinov, A.I. Manevich -- There exist normal Hankel ([symbol], [symbol])-circulants of any order [symbol] / V.N. Chugunov, Kh. D. Ikramov -- On the treatment of boundary artifacts in image restoration by reflection and/or anti-reflection / M. Donatelli, S. Serra-Capizzano -- Zeros of determinants of [symbol]-matrices / W. Gander -- How to find a good submatrix / S.A. Goreinov [und weiteren] -- Conjugate and semi-conjugate direction methods with preconditioning projectors / V.P. Il'in -- Some relationships between optimal preconditioner and superoptimal preconditioner / J.-B. Chen [und weiteren] -- Scaling, preconditioning, and superlinear convergence in GMRES-type iterations / I. Kaporin -- Toeplitz and Toeplitz-block-Toeplitz matrices and their correlation with syzygies of polynomials / H. Khalil, B. Mourrain, M. Schatzman -- Concepts of data-sparse tensor-product approximation in many-particle modelling / H.-J. Flad [und weiteren] -- Separation of variables in nonlinear fermi equation / Yu. I. Kuznetsov -- Faster multipoint polynomial evaluation via structured matrices / B. Murphy, R.E. Rosholt -- Testing pivoting policies in Gaussian elimination / B. Murphy [und weiteren] -- Newton's iteration for matrix inversion, advances and extensions / V.Y. Pan -- Truncated decompositions and filtering methods with reflective/antireflective boundary conditions : a comparison / C. Tablino Possio -- Discrete-time stability of a class of hermitian polynomial matrices with positive semidefinite coefficients / H.K. Wimmer -- Splitting algorithm for solving mixed variational inequalities with inversely strongly monotone operators / I. Badriev, O. Zadvornov -- Multilevel algorithm for graph partitioning / N.S. Bochkarev, O.V. Diyankov, V.Y. Pravilnikov -- 2D-extension of singular spectrum analysis : algorithm and elements of theory / N.E. Golyandina, K.D. Usevich -- Application of radon transform for fast solution of boundary value problems for elliptic PDE in domains with complicated geometry / A.I. Grebennikov -- Application of a multigrid method to solving diffusion-type equations / M.E. Ladonkina, O. Yu. Milukova, V.F. Tishkin -- Monotone matrices and finite volume schemes for diffusion problems preserving non-negativity of solution / I.V. Kapyrin -- Sparse approximation of FEM matrix for sheet current integro-differential equation / M. Khapaev, M. Yu. Kupriyanov -- The method of magnetic field computation in presence of an ideal conductive multiconnected surface by using the integro-differential equation of the first kind / T. Kochubey, V.I. Astakhov -- Spectral model order reduction preserving passivity for large multiport RCLM networks / Yu. M. Nechepurenko, A.S. Potyagalova, I.A. Karaseva -- New smoothers in multigrid methods for strongly nonsymmetric linear systems / G.V. Muratova, E.M. Andreeva -- Operator equations for eddy currents on singular carriers / J. Naumenko -- Matrix approach to modelling of polarized radiation transfer in heterogeneous systems / T.A. Sushkevich, S.A. Strelkov, S.V. Maksakova -- The Method of Regularization of Tikhonov Based on Augmented Systems / A.I. Zhdanov, T.G. Parchaikina

Ordinary Differential Equations And Stability Theory

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Author : David A. Sanchez
language : en
Publisher: Courier Dover Publications
Release Date : 2019-09-18

Ordinary Differential Equations And Stability Theory written by David A. Sanchez and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-18 with Mathematics categories.

This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.

Matrix Methods In Stability Theory

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