title: Stochastic systems with a random jump in phase trajectory: stability of their motions
abstract: 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
keyphrases: stochastic systems random jump phase trajectory general Markov process asymptotic probabilistic stability mean-square exponential stability