A.A. Soliman

Stability criteria of impulsive differential systems

The notion of eventual stability has been recently discussed.We extend this notion to impulsive systems of differential equations. Our technique depends on Liapunovs direct method.

On stability of perturbed impulsive differential systems

The notion of Lipschitz stability of impulsive systems of differential equations (DEs) was introduced. In this paper, we will extend the notion of eventual stability to impulsive systems of DEs and extend the notion of Lipschitz stability of impulsive systems of DEs to a new type of stability called eventual Lipschitz stability. Some criteria and results are given. Our technique depends on Liapunovs direct method and comparison principle.

On perturbing Liapunov functional

Perturbing Liapunov function method was introduced for systems of ordinary differential equations. In this paper, we will extend this method to systems of functional differential equations and discuss stability and boundedness properties via the concept of perturbing Liapunov function.