In this article, the l1l_{1} -induced performance of the stochastic switched Boolean control network (BCN) is investigated. The switched signal is considered to follow a time-varying probability distribution, the switching of which is considered to have a random dwell time. The asynchronous state feedback control (SFC) is studied to achieve the control objective. This kind of control can avoid the failure of the control due to the inconsistency between the system mode and the control mode, so the results obtained are more general. Using the semitensor product of matrices, the algebraic form of the considered BCN is represented. Under this framework, sufficient conditions are obtained to ensure that the closed-loop system is stochastic stabilized with a prescribed l1l_{1} -induced performance level γ\gamma . Parameters can be solved by inequalities. In addition, when the dwell time converges to infinity, the probability distribution of the switched signal becomes fixed. Necessary and sufficient conditions are presented to ensure the stabilization of the closed system under asynchronous SFC as well as the design of the asynchronous SFC. Then, sufficient condition is obtained for the prescribed l1l_{1} -induced performance level. Examples are presented to show the effectiveness of the obtained results.

中文翻译：

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具有分段齐次驻留时间的随机开关布尔控制网络的异步控制


在本文中，研究了随机切换布尔控制网络 (BCN) 的 l1l_{1} 诱导性能。切换信号被认为遵循时变概率分布，其切换被认为具有随机停留时间。研究了异步状态反馈控制(SFC)来实现控制目标。这种控制可以避免由于系统模式与控制模式不一致而导致控制失败，因此得到的结果更具通用性。使用矩阵的半张量积，表示所考虑的 BCN 的代数形式。在此框架下，获得了足够的条件来确保闭环系统在规定的 l1l_{1} 引起的性能水平 γ\gamma 下随机稳定。参数可以通过不等式求解。此外，当驻留时间收敛到无穷大时，切换信号的概率分布变得固定。给出了保证异步SFC下封闭系统稳定性的充要条件以及异步SFC的设计。然后，获得规定的 l1l_{1} 引起的性能水平的充分条件。给出的例子显示了所得结果的有效性。