Boundedness of nonlinear differential systems with impulsive effect on random moments
Consider a system of nonlinear differential equations with impulses at random moments \[ x'(t) = f(t,x(t)) \text{ a.e.}, \quad \xi_{k-1}<t<\xi_k,\;k\in \mathbb{N}, \] \[ x(\xi_k^+)-x(\xi_k)=I_k(\tau_k,x(\xi_k)) \text{ a.e.},\quad k\in \mathbb{N}, \] \[ x(t_0)=x_0, \] where \(\xi_0=t_0\), \(\xi_k=\xi_{k-1}+\tau_k\), and \(\tau_k\) is a random variable for all \(k\in \mathbb{N}\). The authors prove some boundedness results for this system by using Lyapunov-like functions. An example is included, too.
scientific article; zbMATH DE number 2174223