5 edition of **Theory and application of Liapunov"s direct method.** found in the catalog.

- 270 Want to read
- 40 Currently reading

Published
**1963**
by Prentice-Hall in Englewood Cliffs, N.J
.

Written in

- Li͡a︡punov, A. M. 1857-1918.,
- Lyapunov functions.

**Edition Notes**

Statement | English ed. prepared by Siegfried H. Lehnigk. Translation: Hans H. Hosenthien [and] Siegfried H. Lehnigk. |

Series | Prentice-Hall international series in applied mathematics |

Classifications | |
---|---|

LC Classifications | QA871 .H183 |

The Physical Object | |

Pagination | 182 p. |

Number of Pages | 182 |

ID Numbers | |

Open Library | OL5879256M |

LC Control Number | 63009837 |

functions. Lyapunov functions are also basis for many other methods in analysis of dynamical system, like frequency criteria and the method of comparing with other systems. The theory of Lyapunov function is nice and easy to learn, but nding a good Lyapunov function can often be a big scienti c problem. Detecting new e ectiveFile Size: KB. In nonlinear systems, Lyapunov’s direct method (also called the second method of Lyapunov) provides a way to analyze the stability of a system without explicitly solving the differential equations. The method generalizes the idea which shows that the system is stable if there are some Lyapunov function candidates for the by:

In particular, the applications of the ﬁber contraction principle and the Lyapunov–Perron method in this book provide an introduction to some of the basic tools of invariant manifold theory. The theory of averaging is treated from a fresh perspective that is in-tended to introduce the modern approach to this classical subject. A com-. The Lyapunov Second Method Definition of Lyapunov Function We turn now to an entirely different method for studying the stability properties of a given solution. This method, the Lyapunov second method or direct method, uses an approach different from that used in the preceding : Jane Cronin.

, APM Di Equns Intro to Lyapunov theory. Novem 1 1 Lyapunov theory of stability Introduction. Lyapunov’s second (or direct) method provides tools for studying (asymp-totic) stability properties of an equilibrium point of a dynamical system (or systems of dif-ferential equations).File Size: KB. Home» MAA Publications» MAA Reviews» Stability Theory by Liapunov's Direct Method Stability Theory by Liapunov's Direct Method Nicolas Rouche, P. Habets and M. Laloy.

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Theory and Applicaton of Liapunov's Direct Method Theory and application of Liapunovs direct method. book – January 1, by Wolfgang Hahn (Author)Author: Wolfgang Hahn. 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 Cited by: Books; Math & Technical Sciences; Dover Technical; Theory And Application Of Liapunov's Direct Method; Theory And Application Of Liapunov's Direct Method.

Theory And Application Of Liapunov's Direct Method. Author: Hahn, Wolfgang. ISBN: Binding: Paperback. It has remained high ever 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. Theory and Application of Liapunov's Direct Method (Dover Books on Mathematics) by Wolfgang Hahn The groundbreaking work of Russian mathematician A.

Liapunov (–) on the stability of dynamical systems was overlooked for decades because of political turmoil. However, formatting rules can vary widely between applications and fields of interest or study.

The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.

Purchase Stability by Liapunov's Direct Method with Applications by Joseph L Salle and Solomon Lefschetz, Volume 4 - 1st Edition. Print Book & E-Book Book Edition: 1. Journals & Books; Register Sign in. Sign in Register. Journals & Books Latest volume All volumes. Search in this book series. Stability by Liapunov's Direct Method with Applications.

Edited by Joseph La Salle, Solomon Lefschetz. Volume 4, Pages iii-viii, () Download full volume Application of Liapunov's Theory to Controls. Theory and application of Liapunov's direct method. Englewood Cliffs, N.J., Prentice-Hall, (OCoLC) Named Person: A M Li︠a︡punov; A M Lyapunov: Document Type: Book: All Authors / Contributors: Wolfgang Hahn.

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. Lyapunov Direct Method. There are two Lyapunov methods for stability analysis.

Lyapunov direct method is the most effective method for studying nonlinear and time-varying systems and is a basic method for stability analysis and control law desgin. The first method usually requires the analytical solution of the differential equation.

It is an indirect method. Theory and Application of Liapunov's Direct Method; Oscillations in Nonlinear Systems; and Nonlinear Problems Wolfgang Hahn, Editor, H. Lehnigk, Hans H. Hosenthien, Jack K. Hale, Cited by: 4. Lyapunov theory Lyapunov theory is used to make conclusions about trajectories of a system x˙ = f(x) (e.g., G.A.S.) without ﬁnding the trajectories (i.e., solving the diﬀerential equation) a typical Lyapunov theorem has the form: • if there exists a function V: Rn → R that satisﬁes some conditions on V and V˙.

Theory and Application of Liapunov's Direct Method Wolfgang Hahn Stability Theory by Liapunov's Direct Method av Nicolas Rouche, P This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems.

A Review of Fundamentals of Lyapunov Theory. This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear.

Yoshizawa T () Stability theory by Liapunov’s second method. The Mathematical Society of Japan, Tokyo Google Scholar Zubov VI () Methods of A. Lyapunov and their applications. The state variables in the model are the prices of commodities, ρ1,ρN, it is natural to assume that all prices are nonnegative, ρi ≥ 0, i = 1, N; in general it is not excluded that.

The Fast Lyapunov Indicator introduced in Froeschlé et al. (Celest Mech Dyn Astron –62, ) and further developed in Guzzo et al. (Physica D (1–2):1–25, ), is an easy to implement and sensitive tool for the detection of order and chaos in dynamical by: 5.

The contribution to the theory made by N. Chetaev was so significant that many mathematicians, physicists and engineers consider him Lyapunov’s direct successor and the next-in-line scientific descendant in the creation and development of the mathematical theory of stability.

Lyapunov's direct method is employed to prove these stability properties for a nonlinear system and prove stability and convergence. The possible function definiteness is introduced which forms the building block of Lyapunov's direct method.

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.The direct method of Lyapunov.

Lyapunov’s direct method (also called the second method of Lyapunov) allows us to determine the stability of a system without explicitly inte-grating the diﬀerential equation (). The method is a generalization of the idea that if File Size: KB.In the theory of ordinary differential equations (ODEs), Lyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE.

Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov, Lyapunov functions (also called the Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory.