ON THE STABILITY BY THE NONLINEAR NON-STATIONARY HYBRID APPROXIMATION

The paper investigates the effect of non-stationary perturbations on the stability of nonlinear nonautonomous systems with switching and impulsive effects. Sufficient conditions have been obtained to guarantee the asymptotic stability of a given equilibrium position of the initial system, and restrictions have been established under which the asymptotic stability is preserved under perturbations acting on the system. Note that the non-stationarities present both in the system itself and in perturbations can be described by unbounded functions with respect to time, as well as functions arbitrarily close to zero. It is assumed that the basic system is homogeneous in terms of the state vector. To find the required results, the second Lyapunov method is used in combination with the theory of differential inequalities.