Download or read book Theory and Application of Liapunov s Direct Method Hanh written by Wolfgang Hanh and published by . This book was released on 1963 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Theory and application of Liapunov s direct method English ed written by Wolfgang Hahn and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Stability Theory by Liapunov s Direct Method written by Nicolas Rouche and published by . This book was released on 1975 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Application of Lyapunov s Direct Method to Problems of Stability of Non linear Differential Equations Including Control Systems written by J. W. Locker and published by . This book was released on 1966 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Theory and application of Liapunov s direct method written by Wolfgang Hahn and published by . This book was released on 1963 with total page 182 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 Application of the Direct Method of Lyapunov to the Analysis of Control System Performance written by Howell Jack Tipton and published by . This book was released on 1963 with total page 168 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 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lyapunov Stability for Partial Differential Equations Part 1 Lyapunov Stability Theory and the Stability of Solutions to Partial Differential Equations Part 2 Contraction Groups and Equivalent Norms written by and published by . This book was released on 1968 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Theory and application of Liapunov s direct methods written by and published by . This book was released on 1963 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Lyapunov s Direct Method as Applied to Control Engineering Direct Method as Applied to Control Engineering written by Robert Wayne Stubblefield and published by . This book was released on 1964 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Work Session In Lyapunov s Second Method written by and published by . This book was released on 1962 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Control Application of the Direct Method of Lyapunov written by and published by . This book was released on 1963 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lyapunov s Direct Method Extended to Stability of Invariant Sets written by Lawrence Howard Smith and published by . This book was released on 1972 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A New Set of Stability Criteria Extending Lyapunov s Direct Method written by William Li and published by . This book was released on 2020 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: A dynamical system is a mathematical model described by a high dimensional ordinary differential equation for a wide variety of real world phenomena, which can be as simple as a clock pendulum or as complex as a chaotic Lorenz system. Stability is an important topic in the studies of the dynamical system. A major challenge is that the analytical solution of a time-varying nonlinear dynamical system is in general not known. Lyapunov's direct method is a classical approach used for many decades to study stability without explicitly solving the dynamical system, and has been successfully employed in numerous applications ranging from aerospace guidance systems, chaos theory, to traffic assignment. Roughly speaking, an equilibrium is stable if an energy function monotonically decreases along the trajectory of the dynamical system. This paper extends Lyapunov's direct method by allowing the energy function to follow a rich set of dynamics. More precisely, the paper proves two theorems, one on globally uniformly asymptotic stability and the other on stability in the sense of Lyapunov, where stability is guaranteed provided that the evolution of the energy function satisfies an inequality of a non-negative Hurwitz polynomial differential operator, which uses not only the first-order but also high-order time derivatives of the energy function. The classical Lyapunov theorems are special cases of the extended theorems. the paper provides an example in which the new theorem successfully determines stability while the classical Lyapunov's direct method fails.