document: Stochastic systems with a random jump in phase trajectory : stability of their motions The probabilistic stability of the perturbed motion of a system with parameters under the action of a general Markov process is studied . The phase vector is assumed to experience random jumps when the structure the system suffers random jumps . Such a situation is encountered , for example , in the motion of a solid with random jumps in its mass . The mean-square stability of random-structure linear systems and stability . of nonlinear systems in the first approximation are studied . The applied approach is helpful in studying the asymptotic probabilistic stability and mean-square exponential stability of stochastic systems through the stability of the respective deterministic systems
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