Download or read book Applications of Liapunov Methods in Stability written by A. Halanay and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Download or read book Theory and Application of Liapunov s Direct Method written by Wolfgang Hahn and published by Courier Dover Publications. This book was released on 2019-04-17 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stability by Liapunov s Direct Method written by Joseph P. LaSalle and published by . This book was released on 1961 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

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].

Download or read book Methods of A M Lyapunov and Their Application written by Vladimir Ivanovich Zubov and published by . This book was released on 1961 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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."

Download or read book Stability by Liapunov s Direct Method with Applications written by and published by . This book was released on 1961 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability by Liapunov s Direct Method written by J. La Salle and published by . This book was released on 1961 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability by Liapunov s Direct Method written by Joseph P. LaSalle and published by . This book was released on 1961 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability by Liapunov s Direct Method with written by Joseph Pierre LA SALLE (and LEFSCHETZ (Solomon)) and published by . This book was released on 1961 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Application of Liapunov s Direct Method to Stability Problems of Continuous Nonconservative Systems by H H E Leipholz written by Horst H. E. Leipholz and published by . This book was released on 1970 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability by Liapunov s Direct Method written by Joseph La Salle and published by . This book was released on 1961 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability by Liapunov s Direct Methods written by Joseph P. La Salle and published by . This book was released on 1961 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Application of the Liapunov Method to Stability Analysis of Power Systems written by Kendrick A. Williams and published by . This book was released on 1978 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Study of the Application of the Second Method of Liapunov to the Stability of Nonlinear Systems written by James Henry Jones and published by . This book was released on 1959 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: