Stability Analysis For Nonlinear Impulsive Differential Systems

In this dissertation, we study some stability properties for two impulsive differential systems employing Lyapunov's second method: one system is impulsive hybrid differential system:the other is differertial system with impulses at variable time:Herein these stability results do not require a Lyapunov function to have a negative definite first derivative along trajectories of the system, further we may not require its derivative to restrict the function increasing growth; and we do not give conditions on continuous portion or discrete portion of the systems respective!}', hence we can give mixing conditions on them. Base on this idea, we give a series of sufficient conditions to determine stability properties of impulsive differential systems. Firstly, we discuss stability of impulsive hybrid system. Then we obtained the comparison results on stability and eventually uniform stability in terms of two measures for the above system. Lastly , we give sufficient conditions to determine stability in terms of two measures for an differential system with impulsive at varible times.