Stability by Liapunov's Matrix Function Method with Applications

Stability by Liapunov's Matrix Function Method with Applications
Author :
Publisher : CRC Press
Total Pages : 298
Release :
ISBN-10 : 0824701917
ISBN-13 : 9780824701918
Rating : 4/5 (17 Downloads)

Synopsis Stability by Liapunov's Matrix Function Method with Applications by : A.A. Martynyuk

"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."

Stability and Stabilization of Nonlinear Systems with Random Structures

Stability and Stabilization of Nonlinear Systems with Random Structures
Author :
Publisher : CRC Press
Total Pages : 256
Release :
ISBN-10 : 9780203218891
ISBN-13 : 0203218892
Rating : 4/5 (91 Downloads)

Synopsis Stability and Stabilization of Nonlinear Systems with Random Structures by : I. Ya Kats

Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of stability theory and the theory of stabilization of nonlinear systems with random structure in terms of new developments in the direct Lyapunov's method. The analysis focuses on dynamic sys

Dynamics and Stability of Motion of Shock and Hybrid Systems

Dynamics and Stability of Motion of Shock and Hybrid Systems
Author :
Publisher : Walter de Gruyter GmbH & Co KG
Total Pages : 205
Release :
ISBN-10 : 9783110605297
ISBN-13 : 3110605295
Rating : 4/5 (97 Downloads)

Synopsis Dynamics and Stability of Motion of Shock and Hybrid Systems by : Anatoliy A. Martynyuk

Buy this book on degruyter.comhttps://www.degruyter.com/viewbooktoc/product/538686>

Qualitative Methods in Nonlinear Dynamics

Qualitative Methods in Nonlinear Dynamics
Author :
Publisher : CRC Press
Total Pages : 326
Release :
ISBN-10 : 0824707354
ISBN-13 : 9780824707354
Rating : 4/5 (54 Downloads)

Synopsis Qualitative Methods in Nonlinear Dynamics by : A.A. Martynyuk

"Presents new approaches to qualitative analysis of continuous, discreteptime, and impulsive nonlinear systems via Liapunov matrix-valued functions that introduce more effective tests for solving problems of estimating the domains of asymptotic stability."

Applications of Liapunov Methods in Stability

Applications of Liapunov Methods in Stability
Author :
Publisher : Springer Science & Business Media
Total Pages : 245
Release :
ISBN-10 : 9789401116008
ISBN-13 : 9401116008
Rating : 4/5 (08 Downloads)

Synopsis Applications of Liapunov Methods in Stability by : A. Halanay

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.

Qualitative Analysis of Set-Valued Differential Equations

Qualitative Analysis of Set-Valued Differential Equations
Author :
Publisher : Springer
Total Pages : 203
Release :
ISBN-10 : 9783030076443
ISBN-13 : 303007644X
Rating : 4/5 (43 Downloads)

Synopsis Qualitative Analysis of Set-Valued Differential Equations by : Anatoly A. Martynyuk

The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.

Matrix Diagonal Stability in Systems and Computation

Matrix Diagonal Stability in Systems and Computation
Author :
Publisher : Springer Science & Business Media
Total Pages : 279
Release :
ISBN-10 : 9781461213468
ISBN-13 : 1461213460
Rating : 4/5 (68 Downloads)

Synopsis Matrix Diagonal Stability in Systems and Computation by : Eugenius Kaszkurewicz

This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type" Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the spe cial virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors' synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "cul ture" that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonal type Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions. This monograph shows that, although this obvious interpretation is often adequate, there are many in stances in which the Liapunov approach is best taken advantage of using diagonal-type Liapunov functions. In fact, they yield necessary and suffi cient stability conditions for some classes of nonlinear dynamical systems.

Stability of Dynamical Systems

Stability of Dynamical Systems
Author :
Publisher : Elsevier
Total Pages : 719
Release :
ISBN-10 : 9780080550619
ISBN-13 : 0080550614
Rating : 4/5 (19 Downloads)

Synopsis Stability of Dynamical Systems by : Xiaoxin Liao

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

Weakly Connected Nonlinear Systems

Weakly Connected Nonlinear Systems
Author :
Publisher : CRC Press
Total Pages : 228
Release :
ISBN-10 : 9781466570870
ISBN-13 : 1466570873
Rating : 4/5 (70 Downloads)

Synopsis Weakly Connected Nonlinear Systems by : Anatoly Martynyuk

Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected

Mechanical Engineering And Control Systems - Proceedings Of 2015 International Conference (Mecs2015)

Mechanical Engineering And Control Systems - Proceedings Of 2015 International Conference (Mecs2015)
Author :
Publisher : World Scientific
Total Pages : 543
Release :
ISBN-10 : 9789814740623
ISBN-13 : 9814740624
Rating : 4/5 (23 Downloads)

Synopsis Mechanical Engineering And Control Systems - Proceedings Of 2015 International Conference (Mecs2015) by : Xiaolong Li

This book consists of 113 selected papers presented at the 2015 International Conference on Mechanical Engineering and Control Systems (MECS2015), which was held in Wuhan, China during January 23-25, 2015. All accepted papers have been subjected to strict peer review by two to four expert referees, and selected based on originality, ability to test ideas and contribution to knowledge.MECS2015 focuses on eight main areas, namely, Mechanical Engineering, Automation, Computer Networks, Signal Processing, Pattern Recognition and Artificial Intelligence, Electrical Engineering, Material Engineering, and System Design. The conference provided an opportunity for researchers to exchange ideas and application experiences, and to establish business or research relations, finding global partners for future collaborations. The conference program was extremely rich, profound and featured high-impact presentations of selected papers and additional late-breaking contributions.