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Cone-Valued Lyapunov Functions

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Cone-Valued Lyapunov Functions

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Title: Cone-Valued Lyapunov Functions
Author: Leela, S.; Lakshmikantham, V.
Abstract: It is very well known that employing a single Lyapunov function and the theory of scalar differential inequality offers a useful mechanism to study a variety of qualitative problems of differential equations in a unified way [10]. Nevertheless, when using this powerful technique for concrete problems, the main difficulty we face is the lack of general method of constructing a Lyapunov function. This naturally beads to the development of the method of vector Lyapunov functions which utilizes several Lyapunov-like functions and the theory of vector differential inequalities in a fruitful manner [5,8-12]. This method offers a more flexible mechanism to discuss qualitative properties of nonlinear systems. Also, it provides an effective tool to investigate the properties of large scale interconnected dynamical and control systems whose multivariability, composite structure, multi-connection and the variety of the nature of subsystems make the construction of a single Lyapunov function much more difficult. Moreover, several Lyapunov functions result in a natural way in the study of such systems by the decomposition and aggregation method [1,3,5,6,13-15].
URI: http://hdl.handle.net/10106/2205
Date: 1976-08

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