Continuing the strong tradition of functional analysis and stability theory for differential and integral equations already established by the previous volumes in this series, this innovative monograph considers in detail the method of limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed. For the first time, the method first employed by Krylov and Bogolubov in their investigations of oscillations in almost linear systems is applied to a new field: that of the stability problem of systems with small parameters. This important development should facilitate the solution of engineering problems in such areas as orbiting satellites, rocket motion, high-speed vehicles, power grids, and nuclear reactors.
Table of Contents
Introduction to the Series, Foreword, Preface to the English edition, Notation, 1 Stability Analysis of ODEs by the Method of Limiting Equations, 2 Limiting Equations and Stability of Infinite Delay Systems, 3 Limiting Systems and Stability of Motion under Small Forces, 4 Stability Analysis of Solutions of ODEs (Continued), 5 Stability of Integro-Differential Systems, 6 Optimal Stabilization of Controlled Motion and Limiting Equations, 7 Stability of Abstract Compact and Uniform Dynamical Processes, 8 Stability in Abstract Dynamical Processes on Convergence Space, 9 Limiting Lyapunov Functionals for Asymptotically Autonomous Evolutionary Equations of Parabolic and Hyperbolic Type in a Banach Space, References, Index
Professor Kato is based at the Mathematical Institute at Tohoku University in Japan where he actively pursues his research interest in the field of stability of motion. Professor Martynyuk has headed the Stability of Processes Division at the Institute of Mechanics in Kiev since 1978. His main research interests include theory of stability of motion of systems modelled by ordinary and partial differential equations, control of motion, and theory of large-scale systems. Professor Shestakov is also involved in research into stability and control at the Institute of Railway Transport in Moscow.