Electron. J. Diff. Equ., Vol. 2010(2010), No. 78, pp. 1-18.

Lyapunov stability of closed sets in impulsive semidynamical systems

Everaldo M. Bonotto, Nivaldo G. Grulha Jr.

Abstract:
In this article, we consider impulsive semidynamical systems, defined in a metric space, with impulse effects at variable times. Converse-type theorems are included in our results giving necessary and sufficient conditions for various types of stability of closed subsets of the metric space. These results are achieved by means of Lyapunov functionals which indicate how the solutions behave when entering a "stable" set.

Submitted September 8, 2009. Published June 8, 2010.
Math Subject Classifications: 34A37, 37B25, 54H20.
Key Words: Impulsive semidynamical systems; stability; Lyapunov functionals.

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Everaldo M. Bonotto
Instituto de Ciências Matemáticas e de Computação
Universidade de São Paulo-Campus de São Carlos
Caixa Postal 668, 13560-970, São Carlos SP, Brazil
email: ebonotto@icmc.usp.br
Nivaldo G. Grulha Jr.
Instituto de Ciências Matemáticas e de Computação
Universidade de São Paulo-Campus de São Carlos
Caixa Postal 668, 13560-970, São Carlos SP, Brazil
email: njunior@icmc.usp.br

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