Qualitative methods in nonlinear dynamics : novel approaches to Liapunov's matrix functions

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Qualitative methods in nonlinear dynamics : novel approaches to Liapunov's matrix functions / A.A. Martynyuk

資料種別:: 図書
出版情報:: New York : Marcel Dekker, c2002
形態:: x, 301 p. ; 24 cm
シリーズ名:: Monographs and textbooks in pure and applied mathematics ; 246 <BA00046446>
著者名:: Martyni︠u︡k, A. A. (Anatoliĭ Andreevich) <DA01878225>
ISBN:: 9780824707354 [0824707354]
書誌ID:: BA54465930

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注記:

Bibliography: p. 277-294
Includes index

言語:

英語

目次情報:

Preface

Preliminaries / 1：

Introduction / 1.1：

Nonlinear Continuous Systems / 1.2：

General equations of nonlinear dynamics / 1.2.1：

Perturbed motion equations / 1.2.2：

Definitions of Stability / 1.3：

Scalar, Vector and Matrix-Valued Liapunov Functions / 1.4：

Auxiliary scalar functions / 1.4.1：

Comparison functions / 1.4.2：

Vector Liapunov functions / 1.4.3：

Matrix-valued metafunction / 1.4.4：

Comparison Principle / 1.5：

Liapunov-Like Theorems / 1.6：

Matrix-valued function and its properties / 1.6.1：

A version of the original theorems of Liapunov / 1.6.2：

Advantages of Cone-Valued Liapunov Functions / 1.7：

Stability with respect to two measures / 1.7.1：

Stability analysis of large scale systems / 1.7.2：

Liapunov's Theorems for Large Scale Systems in General / 1.8：

Why are matrix-valued Liapunov functions needed? / 1.8.1：

Stability and instability of large scale systems / 1.8.2：

Notes / 1.9：

Qualitative Analysis of Continuous Systems / 2：

Nonlinear Systems with Mixed Hierarchy of Subsystems / 2.1：

Mixed hierarchical structures / 2.2.1：

Hierarchical matrix function structure / 2.2.2：

Structure of hierarchical matrix function derivative / 2.2.3：

Stability and instability conditions / 2.2.4：

Linear autonomous system / 2.2.5：

Examples of third order systems / 2.2.6：

Dynamics of the Systems with Regular Hierarchy Subsystems / 2.3：

Ikeda-Siljak hierarchical decomposition / 2.3.1：

Hierarchical Liapunov's matrix-valued functions / 2.3.2：

Linear nonautonomous systems / 2.3.3：

Stability Analysis of Large Scale Systems / 2.4：

A class of large scale systems / 2.4.1：

Construction of nondiagonal elements of matrix-valued function / 2.4.2：

Test for stability analysis / 2.4.3：

Linear large scale system / 2.4.4：

Discussion and numerical example / 2.4.5：

Overlapping Decomposition and Matrix-Valued Function Construction / 2.5：

Dynamical system extension / 2.5.1：

Liapunov matrix-valued function construction / 2.5.2：

Test for stability of system (2.5.1) / 2.5.3：

Numerical example / 2.5.4：

Exponential Polystability Analysis of Separable Motions / 2.6：

Statement of the Problem / 2.6.1：

A method for the solution of the problem / 2.6.2：

Autonomous system / 2.6.3：

Polystability by the first order approximations / 2.6.4：

Integral and Lipschitz Stability / 2.7：

Definitions / 2.7.1：

Sufficient conditions for integral and asymptotic integral stability / 2.7.2：

Uniform Lipschitz stability / 2.7.3：

Qualitative Analysis of Discrete-Time Systems / 2.8：

Systems Described by Difference Equations / 3.1：

Matrix-Valued Liapunov Functions Method / 3.3：

Auxiliary results / 3.3.1：

Comparison principle application / 3.3.2：

General theorems on stability / 3.3.3：

Large Scale System Decomposition / 3.4：

Stability and Instability of Large Scale Systems / 3.5：

Auxiliary estimates / 3.5.1：

Autonomous Large Scale Systems / 3.5.2：

Hierarchical Analysis of Stability / 3.7：

Hierarchical decomposition and stability conditions / 3.7.1：

Novel tests for connective stability / 3.7.2：

Controlled Systems / 3.8：

Nonlinear Dynamics of Impulsive Systems / 3.9：

Large Scale Impulsive Systems in General / 4.1：

Notations and definitions / 4.2.1：

Sufficient stability conditions / 4.2.2：

Instability conditions / 4.2.4：

Hierarchical Impulsive Systems / 4.3：

Analytical Construction of Liapunov Function / 4.4：

Structure of hierarchical matrix-valued Liapunov function / 4.4.1：

Structure of the total derivative of hierarchical matrix-valued function / 4.4.2：

Uniqueness and Continuability of Solutions / 4.5：

On Boundedness of the Solutions / 4.6：

Novel Methodology for Stability / 4.7：

Stability conditions / 4.7.1：

Applications / 4.8：

Estimations of Asymptotic Stability Domains in General / 5.1：

A fundamental Zubov's result / 5.2.1：

Some estimates for quadratic matrix-valued functions / 5.2.2：

Algorithm of constructing a point network covering boundary of domain E / 5.2.3：

Numerical realization and discussion of the algorithm / 5.2.4：

Illustrative examples / 5.2.5：

Construction of Estimate for the Domain E of Power System / 5.3：

Oscillations and Stability of Some Mechanical Systems / 5.4：

Three-mass systems / 5.4.1：

Nonautonomous oscillator / 5.4.2：

Absolute Stability of Discrete Systems / 5.5：

References / 5.6：

Subject Index

Preface

Preliminaries / 1：

Introduction / 1.1：

Nonlinear Continuous Systems / 1.2：

General equations of nonlinear dynamics / 1.2.1：

Perturbed motion equations / 1.2.2：

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