Lyapunov function method for investigation of stability of stochastic Ito random-structure systems with impulse Markov switchings. I. General theorems on the stability of stochastic impulse systems

The asymptotic stochastic stability on the whole and asymptotic p-stability on the whole are investigated with the help of Lyapunov functions and the concept of an infinitesimal operator over solutions to a system (to calculate this operator, it suffices to know only the coefficients of the system). The stability under constant perturbations is considered.