Overview

The problems of modern society are both complex and multidisciplinary. In spite of the apparent diversity of problems, tools developed in one context are often adaptable to an entirely different situation. The concepts of Lyapunov stability have given rise to many new notions that are important in applications. Relative to each concept, there exists a sufficient literature parallel to Lyapunov's theory of stability. It is natural to ask whether we can find a notion and develop the corresponding theory which unifies and includes a variety of known concepts of stability in a single set up. The answer is yes and it is the development of stability theory in terms of two measures. It is in this spirit the authors see the importance of the present monograph. Its aim is to present a systematic account of recent developments in the stability theory in terms of two distinct measures, describe the current state of the art, show the essential unity achieved by wealth of applications, and provide a unified general structure applicable to several nonlinear problems.Contents: Basic Theory: Definitions of StabilityBasic Lyapunov TheoryComparison MethodConverse TheoremBoundedness and Lagrange StabilityInvariance Principle Refinements: Several Lyapunov FunctionsPerturbations of Lyapunov FunctionsMethod of Vector Lyapunov FunctionsPerturbed SystemsIntegral StabilityMethod of Higher DerivativesCone-Valued Lyapunov Functions Extensions: Delay Differential EquationsImpulsive Differential SystemsStabilization of Control SystemsImpulsive Integro-Differential SystemsDiscrete SystemsRandom Differential SystemsDynamic Systems on Time Scales Applications: Holomorphic Mechanical SystemsMotion of Winged AircraftModels from EconomicsMotion of a Length-Varying PendulumPopulation ModelsAngular Motion of Rigid BodiesReadership: Applied Mathematicians.

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