Stability analysis in terms of two measures
著者
書誌事項
Stability analysis in terms of two measures
World Scientific, c1993
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- Part 1 Basic theory: definitions of stability
- basic Lyapunov theory
- comparison method
- converse theorem
- boundedness and Lagrange stability
- invariance principle. Part 2 Refinements: several Lyapunov functions
- perturbations of Lyapunov functions
- method of vector Lyapunov functions
- perturbed systems
- integral stability
- method of higher derivatives
- cone-valued Lyapunov functions. Part 3 Extensions: delay differential equations
- impulsive differential systems
- stabilization of control systems
- impulsive integro-differential systems
- discrete systems
- random differential systems
- dynamic systems on time scales. Part 4 Applications: holomorphic mechanical systems
- motion of winged aircraft
- models from economics
- motion of a length-varying pendulum
- population models
- angular motion of rigid bodies.
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