This volume presents surveys and research papers on various aspects of modern stability theory, including discussions on modern applications of the theory, all contributed by experts in the field. The volume consists of four sections that explore the following directions in the development of stability theory: progress in stability theory by first approximation; contemporary developments in Lyapunov's idea of the direct method; the stability of solutions to periodic differential systems; and selected applications. Advances in Stability Theory at the End of the 20th Century will interest postgraduates and researchers in engineering fields as well as those in mathematics.
Introduction to the Series. Preface. Overview. Progress in Stability Theory by the First Approximation. Invariant Foliations for Caratheodory Type Differential Equations. On Exponential Asymptotic Stability for Functional Differential Equations with Causal Operators. Lyapunov Problems on Stability. Contemporary Development of Lyapunov's Ideas of Direct Method. Vector Lyapunov Function: Nonlinear, Time-Varying, Ordinary and Functional Differential Equations. Some Results on Total Stability Properties for Singular Systems. Stability Theory of Voltera Difference Equations. Consistent Lyapunov Methodology for Exponential Stability: PCUP Approach. Advances in Stability Theory of Lyapunov: Old and New. Matrix Lyapunov Functions and Stability Analysis of Dynamical Systems. Stability Theorems in Impulsive Functional Differential Equations with Infinite Delay. The Asymptotic Behavior of Solutions of Stochastic Functional Differential Equations with Finite Delays by Lyapunov-Razumikhin Method. A Non-standard Approach to the Study of the Dynamic System Stability. Stability of Solutions. A Survey of Starzhinskii's Works on Stability of Periodic Motions and Nonlinear Oscillations. Implications of the Stability of an Orbit for Its Omega Limit Set. Some Concepts of Periodic Motions and Stability Originated by Analysis of Homogenous Systems. Stability Criteria for Periodic Solutions of Autonomous Hamiltonian Systems. Selected Applications. Stability in Models of Agriculture-Industry-Environment. Bifurcations of Periodic Solutions of the Three Body Problem. Complex Mechanical Systems: Steady State Motions, Oscillations, Stability. Progress in Stability of Impulsive Systems with Applications to Population Growth Models. Contemporary Development of Lyapunov's Ideas of Direct Method. Stability of Solutions to Periodic Differential Systems. Selected Applications.