Stability and boundedness criteria of nonlinear impulsive systems employing perturbing Lyapunov functions (Q555447)

The authors consider a nonlinear dynamical system in a real \(n\)-dimensional Euclidean space of the form \[ \begin{aligned} x'= f(t,x),\quad & t\neq t_k,\\ \Delta x= I_k(x),\quad & t= t_k,\\ x(t^+_0)= x_0,\quad & t_0\geq 0,\;k= 1,2,3,\dots\;.\end{aligned}\tag{1} \] Many notions of stability for (1) are introduced. Sufficiently conditions for these stabilities are found.