Download for FREE in 4 easy steps...
You can also read this in Bookboon.com Premium
The monograph presents a generalization of the well-known Lyapunov function method and related concepts to the matrix function case within systematic stability analysis of dynamical systems.
300+ Business books exclusively in our Premium eReader
- No adverts
- Advanced features
- Personal library
Users who viewed this item also viewed
Stability Analysis via Matrix Functions Method - Part II
Discrete Dynamical Systems - with an Introduction to Discrete Optimization Problems
Quantitative Analysis - Algebra with a Business Perspective
Advanced stochastic processes: Part I
Stability, Riemann Surfaces, Conformal Mappings - Complex Functions Theory a-3
Matematisk Analyse 4b - Metoder ved opgaveregning i Fourierækker, Differentiallignin
Partial differential equations and operators - Fundamental solutions and semigroups Part II
Matrix Methods and Differential Equations - A Practical Introduction
About the book
The monograph presents a generalization of the well-known Lyapunov function method and related concepts to the matrix function case within the framework of systematic stability analysis of dynamical systems (differential equations). Applications are provided with stability issues of ordinary differential equations, singularly perturbed systems, and stochastic differential equations up to some applications to so-called real world situations.
The book is organized in five chapters. Each chapter is accompanied by numerous examples and notes on the locally related bibliography. This book is very innovative and systematically developed and rich on new ideas in contemporary stability theory.
Thus it can be recommended to any specialist in nonlinear dynamical systems and differential equations, both in deterministic and stochastic analysis.
One can hardly name a branch of natural science or technology in which the problems of stability do not claim the attention of scholars, engineers, and experts who investigate natural phenomena or operate designed machines or systems. If, for a process or a phenomenon, for example, atom oscillations or a supernova explosion, a mathematical model is constructed in the form of a system of differential equations, the investigation of the latter is possible either by a direct (numerical as a rule) integration of the equations or by its analysis by qualitative methods.
The direct Liapunov method based on scalar auxiliary function proves to be a powerful technique of qualitative analysis of the real world phenomena. This volume examines new generalizations of the matrix-valued auxiliary function. Moreover the matrix-valued function is a structure the elements of which compose both scalar and vector Liapunov functions applied in the stability analysis of nonlinear systems.
Due to the concept of matrix-valued function developed in the book, the direct Liapunov method becomes yet more versatile in performing the analysis of nonlinear systems dynamics.
The possibilities of the generalized direct Liapunov method are opened up to stability analysis of solutions to ordinary differential equations, singularly perturbed systems, and systems with random parameters.
The reader with an understanding of fundamentals of differential equations theory, elements of motion stability theory, mathematical analysis, and linear algebra should not be confused by the many formulas in the book. Each of these subjects is a part of the mathematics curriculum of any university.
In view of the fact that beginners in motion stability theory usually face some difficulties in its practical application, the sets of problems taken from various branches of natural sciences and technology are solved at the end of each chapter. The problems of independent value are integrated in Chapter 5.
- On Definition of Stability
- Brief Outline of Trends in Liapunov’s Stability Theory
- Matrix Liapunov Function Method in General
- Definition of Matrix-Valued Liapunov Functions
- Direct Liapunov’s Method in Terms of Matrix-Function
- On Comparison Method
- Method of Matrix Liapunov Functions
- On Multistability of Motion
- Stability of Singularly-Perturbed Systems
- Description of Systems
- Asymptotic Stability Conditions
- Singularly Perturbed Lur’e-Postnikov Systems
- The Property of Having a Fixed Sign of Matrix-Valued Function
- Matrix-Valued Liapunov Function
- General Theorems on Stability and Instability in Case A
- General Theorems on Stability and Instability in Case B
- Asymptotic Stability of Linear Autonomous Systems
About the Author
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.
The embed frame is free to use for private persons, universities and schools. It is not allowed to be used by any company for commercial purposes unless it is for media coverage. You may not modify, build upon, or block any portion or functionality of the embed frame, including but not limited to links back to the bookboon.com website.
The Embed frame may not be used as part of a commercial business offering. The embed frame is intended for private people who want to share eBooks on their website or blog, professors or teaching professionals who want to make an eBook available directly on their page, and media, journalists or bloggers who wants to discuss a given eBook
If you are in doubt about whether you can implement the embed frame, you are welcome to contact Thomas Buus Madsen on email@example.com and seek permission.