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Stability on a cone in terms of two measures for impulsive differential equations with “supremum”

✍ Scribed by Snezhana G. Hristova

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
245 KB
Volume
23
Category
Article
ISSN
0893-9659

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✦ Synopsis

The stability of nonlinear impulsive differential equations with ''supremum'' is studied. A special type of stability, combining two different measures and a dot product, is defined. The definition is a generalization of several types of stability known in the literature. Razumikhin's method as well as a comparison method for scalar impulsive ordinary differential equations have been employed.

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In this work, we consider a new approach to the practical stability theory of impulsive functional differential equations. With Lyapunov functionals and Razumikhin technique, we use a new technique in the division of Lyapunov functions, given by Shunian Zhang, and obtain conditions sufficient for th