Strict stability in terms of two measures for impulsive differential equations with ‘supremum’

Abstract

Strict stability for a nonlinear system of impulsive differential equations with ‘supremum’ is defined and studied. Razhumikhin method with piecewise continuous scalar Lyapunov functions and comparison results for scalar impulsive differential equations are the bases of the main proofs. To unify a variety of stability concepts and to offer a general framework for the investigation of the stability theory, the notion of stability in terms of two measures has been applied. An example illustrating the usefulness of the obtained sufficient conditions is also included.

Keywords:

• strict stability
• two measures
• piecewise continuous Lyapunov functions
• impulses
• differential equations with ‘supremum’

AMS Subject Classification:

• 34D20

Acknowledgements

The research was partially supported by the Grant MU11FMI005/29.05.2011.