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Stability of Weakly Connected Nonlinear Systems

Stability of Weakly Connected Nonlinear Systems
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ISBN: 978-87-403-1859-3
1. Auflage
Seiten : 267
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Über das Buch

  1. Beschreibung
  2. Inhalt

Beschreibung

The book consists of five chapters in which the mathematical foundations of the analysis of the stability of systems with a small parameter are given as well as methods of their investigation. The proposed methods are based on nonlinear integral inequalities, the direct Lyapunov method, using scalar, vector and matrix-valued functions, as well as the method of averaging of nonlinear mechanics. Here we also obtain sufficient conditions for various types of boundedness and stability of motion of nonlinear weakly connected systems, including systems of equations in a Banach space.

About the authors

A.A.Martynyuk is Professor and academician of the National Academy of Sciences of Ukraine Head of Stability of Processes Department at the S.P.Timoshenko Institute of Mechanics of NAS of Ukraine. The author or coauthor of more than 350 journal publications and 26 of books published in Russian, English and Chinese. He is founder and Editor of the International Journal of Nonlinear Dynamics and Systems Theory and the International Series of Scientific Monographs: Stability, Oscillations and Optimization of Systems published by the Cambridge Scientific Publishers (United Kingdom). He received D.Sc.degree (1973) in physics and mathematics from Institute of Mathematics NAS of Ukraine, Kiev. For more information see please www.martynyuk.kiev.ua.

L.N. Chernetskaya is a senior research fellow of the Department of Processes Stability of the Institute of Mechanics of the National Academy of Sciences of Ukraine. The author (co-author) of more than 100 scientific works in the field of theories of stability and motion control. Thesis defended in 1986 in the Institute of Mechanics of the National Academy of Sciences of Ukraine.

V.A. Martynyuk is a specialist in the field of nonlinear dynamics of weekly connected systems. He is the author of several scientific works published in Journal of Mathematical Analysis and Applications (USA) and International Applied Mechanics (Ukraine).

Inhalt

  1. Preliminaries 
    1. Introductory Remarks 
    2. Fundamental Inequalities 
    3. Stability in the Sense of Lyapunov 
    4. Comparison Principle 
    5. Stability of Systems with a Small Parameter 
    6. Comments and References 
  2. Analysis of the Boundedness of Motion 
    1. Introductory Remarks 
    2. Statement of the Problem 
    3. μ-Boundedness with Respect to Two Measures 
    4. Boundedness and the Comparison Technique 
    5. Boundedness with Respect to a Part of Variables 
    6. Algebraic Conditions of μ-Boundedness 
    7. Applications 
    8. Comments and References 
  3. Analysis of the Stability of Motion 
    1. Introductory Remarks 
    2. Statement of the Problem 
    3. Stability with Respect to Two Measures 
    4. Equistability Via Scalar Comparison Equations 
    5. Dynamic Behavior of an Individual Subsystem 
    6. Asymptotic Behavior 
    7. Polystability of Motion 
    8. Applications 
    9. Comments and References 
  4. Stability of Weakly Perturbed Systems 
    1. Introductory Remarks 
    2. Averaging and Stability 
    3. Stability on a Finite Time Interval 
    4. Methods of Application of Auxiliary Systems 
    5. Systems with Nonasymptotically Stable Subsystems 
    6. Stability with Respect to a Part of Variables 
    7. Applications 
    8. Comments and References 
  5. Stability of Systems in Banach Spaces 
    1. Introductory Remarks 
    2. Preliminary Results 
    3. Statement of the Problem 
    4. Generalized Direct Lyapunov Method 
    5. μ-Stability of Motion of Weakly Connected Systems 
    6. Stability Analysis of a Two-Component System 
    7. Comments and References 

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