In this paper, we consider the stochastically finite-time control problem for a class of positive stochastic Poisson jump systems (PSPJSs). By introducing a novel mode decoupling technique, some necessary and sufficient conditions are given to guarantee the stochastic finite-time boundedness of the input-free PSPJSs. Then, a proper mode-dependent finite-time state feedback controller is designed such that the positiveness, stochastic finite-time boundedness and the specified disturbance attenuation performance are attained simultaneously for the closed-loop SPJSs. Finally, two examples are given to show the feasibility and validity of the proposed methods.

中文翻译：

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正随机泊松跳跃系统有限时间控制的充要条件

在本文中，我们考虑一类正随机泊松跳跃系统（PSPJS）的随机有限时间控制问题。通过引入一种新颖的模式解耦技术，给出了保证无输入 PSPJS 的随机有限时间有界性的一些充要条件。然后，设计了一种合适的模态相关有限时间状态反馈控制器，使得闭环SPJS同时获得正性、随机有限时间有界性和指定的扰动衰减性能。最后通过两个算例说明了所提方法的可行性和有效性。