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Stability Theory of Large-Scale Dynamical Systems

by A. A. Martynyuk V. G. Miladzhanov
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Language:  English
This book focuses on some problems of stability theory of nonlinear large-scale systems.
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Content

This book focuses on some problems of stability theory of nonlinear large-scale systems. The purpose of this book is to describe some new applications of Lyapunov matrix-valued functions method to the stability of evolution problems governed by nonlinear continuous systems, discrete-time systems, impulsive systems and singularly perturbed systems under structural perturbations. The authors take a challenging and original approach based on concept of structural perturbations combined with direct Lyapunov's method. This new approach will lead to results that cannot be obtained by standard theories of stability in the field.

The Stability Theory of Large Scale Dynamical Systems addresses to specialists in dynamical systems, applied differential equations, and the stability theory. It may be useful for graduated students in mathematics, control theory, and mechanical engineering.

  1. Generalities
    1. Introduction
    2. Some Types of Large-Scale Dynamical Systems
    3. Structural Perturbations of Dynamical Systems
    4. Stability under Nonclassical Structural Perturbations
    5. Method of Stability Analysis of Motion
    6. Notes and References
  2. Continuous Large-Scale Systems
    1. Introduction
    2. Nonclassical Structural Perturbations in Time-Continuous Systems
    3. Estimates of Matrix-Valued Functions
    4. Tests for Stability Analysis
    5. Linear Systems Analysis
    6. Certain Trends of Generalizations and Applications
    7. Notes and References
  3. Discrete-Time Large-Scale Systems
    1. Introduction
    2. Nonclassical Structural Perturbations in Discrete-Time Systems
    3. Liapunov’s Matrix-Valued Functions
    4. Tests for Stability Analysis
    5. Certain Trends of Generalizations and Applications
    6. Notes and References
  4. Impulsive Large-Scale Systems
    1. Introduction
    2. Nonclassical Structural Perturbations in the Impulsive Systems
    3. Definitions of Stability
    4. Tests for Stability and Instability Analysis
    5. Linear Systems Analysis
    6. Certain Trends of Generalizations and Applications
    7. Notes and References
  5. Singularly Perturbed Large-Scale Systems
    1. Introduction
    2. Nonclassical Structural Perturbations in Singularly Perturbed Systems
    3. Tests for Stability Analysis
    4. Tests for Instability Analysis
    5. Linear Systems
    6. Certain Trends of Generalizations and Applications
    7. Notes and References
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About the Authors
A.

A. A. Martynyuk

Martynyuk is organizer and head of the Department of Processes Stability at the S.P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (NAS of Ukraine) since 1978.  

He developed the method of Lyapunov matrix functions as applied to uncertain systems, systems with fuzzy information, and dynamic equations on time scales, non-classical theories of stability of motion, chaotic dynamics, and mathematical ecology. 

As the editor of a series of scientific monographs "Stability and Control: Theory, Methods and Applications" (1995-2002) at the publishing house Gordon and Breach (UK) and Taylor and Francis (USA) he organized the work of scientists from many countries of the world to create the series consist with 22 volumes, which opened new opportunities for young scientists to continue research in many areas of research in the qualitative theory of equations. 

He is currently focusing on the publication of a series of scientific monographs "Stability, Oscillation and Optimization of Systems" at the publishing house Cambridge Scientific Publishers (UK). 

Martynyuk is the founder and editor-in-chief of the International Scientific Journal "Nonlinear Dynamics and Systems Theory", which is well known throughout the world. 

He is the author (co-author) of a number of monographs in Russian, English and Chinese. 

He is a doctor of physical and mathematical sciences, professor, academician of the NAS of Ukraine, laureate of the State Prize of Ukraine in the field of science and technology. 

Martynyuk is based in Ukraine, but he actively communicates with experts from all over the world that are interested in stability theory and motion control in the study of real-world phenomena.

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V. G. Miladzhanov

Professor V.G.Miladzhanov died unexpectedly on May 13, 2013 at the age of 60. Scientific results of Professor Miladzhanov are associated with the development of the method of matrix Lyapunov functions for stability investigation of systems with quick and slow motions; stability analysis of large-scale continuous systems ; stability analysis of large-scale discrete systems ; stability of impulsive system under structural perturbations. He proposed a method of constructing hierarchical matrix Lyapunov function for non-autonomous systems which is used in stability investigation of nonlinear mechanical systems.

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