Comparison System Method for a class of Stochastic Systems with Variable-time Impulses
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2018, Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature. This paper studies the stability of stochastic impulsive systems with variable-time impulses. We consider the case that the trajectory of the stochastic system intersects each surface of discontinuity exactly once. Then we shall show that under the well-selected conditions the variable-time impulsive systems can be reduced to the fixed-time impulsive systems with impulse time window. By using comparison method, we obtain two theorems to determine the different impulsive time windows for stable and unstable stochastic dynamical systems, respectively. The effectiveness of the theoretical results are illustrated by two numerical examples.