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This paper is concerned with the finite-time annular domain bounded control of Itô-type stochastic systems with wiener and poisson random disturbance. First, utilizing different quadratic function methods, some sufficient conditions for finite-time annular domain bounded-ness (FTADB) of the system are achieved. Second, two finite-time annular domain bounded controllers are skillfully developed to ensure the FTADB of the closed-loop system, of which one is state feedback controller and the other is dynamic output feedback controller. Furthermore, an algorithm is provided to deal with the obtained matrix inequalities. Finally, two examples are used to demonstrate the effectiveness of the theorems in this paper.INDEX TERMS stochastic systems, poisson random disturbance, finite-time annular domain bounded.