Stability Analysis Of Impulsive Differential Systems

In this dissertation, we st U(ly some stability 1)mPeli ics iii terms of two inca? sures loi?impulsive d~{[ereiitial Systems elnl)loying Lyapuiiov 慡 SCC.ofl(l nietbod. 1-lcreiu these stability results do not require a Lyapunov function to have a iiegative definite derivative along trajectories of the system, but allow for cas- es where Lyapunov function may increase during the continmous portion of the trajectories or may experience a. jump increase at the impulse. Nonetheless, conditions on Lyapunov function must be placed to ensure that. its growth is not too rapid. Based oii this idea we give a series of suf[iceut conditions to (leternhille property of i nipuls i VU (Ii fFcrentia.l systems. Firstly, we (liscuss sta- bility, bouncledness, prati cal stability and cventua.l stability for an differential system with impulses a.t fixed times by the generalized second (lerivative of Lyapunov function. Then we give another two kinds oi conclitiomis to 1扖S1)CC- tively determine uniform asymptotic stability, exj.onential asymptotic stability and Lagrange stability h)m?the above systenm. Lastly, by virtue of a comparison I)ri1~ciplc in [12], we ol)taille(l time comparison res ults on stability and eventu- ally uniform asymptotic stal)ihity iii terms of two measures for an differential system with impulses at variable times.