Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion

Preliminaries
Introductory Remarks
Fundamental Inequalities
Stability in the Sense of Lyapunov
Comparison Principle
Stability of Systems with a Small Parameter

Analysis of the Boundedness of Motion
Introductory Remarks
Statement of the Problem
μ-Boundedness with Respect to Two Measures
Boundedness and the Comparison Technique
Boundedness with Respect to a Part of Variables
Algebraic Conditions of μ-Boundedness
Applications

Analysis of the Stability of Motion
Introductory Remarks
Statement of the Problem
Stability with Respect to Two Measures
Equistability via Scalar Comparison Equations
Dynamic Behavior of an Individual Subsystem
Asymptotic Behavior
Polystability of Motion
Applications

Stability of Weakly Perturbed Systems
Introductory Remarks
Averaging and Stability
Stability on a Finite Time Interval
Methods of Application of Auxiliary Systems
Systems with Nonasymptotically Stable Subsystems
Stability with Respect to a Part of Variables
Applications

Stability of Systems in Banach Spaces
Introductory Remarks
Preliminary Results
Statement of the Problem
Generalized Direct Lyapunov Method
μ-Stability of Motion of Weakly Connected Systems
Stability Analysis of a Two-Component System

Bibliography

Index