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1.

図書

図書
A.A. Martynyuk
出版情報: New York : Marcel Dekker, c2002  x, 301 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 246
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目次情報: 続きを見る
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:
2.

図書

図書
Lj.T. Grujić, A.A. Martynyuk, M. Ribbens-Pavella
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  xvi, 366 p. ; 24 cm
シリーズ名: Lecture notes in control and information sciences ; 92
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3.

図書

図書
V. Lakshmikantham, S. Leela, A.A. Martynyuk
出版情報: New York : M. Dekker, c1989  ix, 315 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 125
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4.

図書

図書
V. Lakshmikantham, S. Leela, A.A. Martynyuk
出版情報: Singapore ; Teaneck, N.J. : World Scientific, c1990  viii, 207 p. ; 22 cm
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