Stability analysis for systems with impulse effects (Q870788)

The authors consider the impulsive differential equation \[ \frac {dx} {dt}=f(t,x),\;t\neq\tau_k \] \[ \Delta x=I_k(x),\;t=\tau_k,\;f(0,t)= I_k(0)=0\text{ for }t\in \mathbb{R}^+,k=1,2,\dots \] in the space \(X=\mathbb{R}^n\). Sufficient conditions for the uniform asymptotic stability of the equilibrium point \(x=0\) are derived.