This paper considers the problems of stabilization and H∞ control for fast sampling discrete-time singularly perturbed singular Markovian systems (SPSMSs). The system equivalent approach is initially introduced to transform the discrete fast sampling SPSMS model into the augmented SPSMS for the convenience of designing system controller. Secondly, sufficient condition on stochastically mean square admissibility is established for the fast sampling SPSMS. By separating matrix variables and singularly perturbed parameter, a state feedback controller is also provided to ensure stochastically mean square admissibility of the fast sampling augmented SPSMS. Then, the results are extended to H∞ performance analysis and controller design in the presence of the external disturbances. The derived criteria can be converted to the feasible problems based on convex optimization, and the upper bound of singular perturbation parameter is also calculated. Besides, a discretized electrical circuit system is provided to verify the effectiveness and the superiority of the proposed approach.

中文翻译：

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快速采样离散时间奇异扰动奇异马尔可夫系统的稳定性


本文考虑了快速采样离散时间奇异扰动奇异马尔科夫系统 （SPSMS） 的稳定性和 H∞ 控制问题。最初引入系统等效方法，将离散快速采样 SPSMS 模型转换为增强的 SPSMS，以方便设计系统控制器。其次，为快速采样 SPSMS 建立了随机均方可接受性的充分条件。通过分离矩阵变量和奇异扰动参数，还提供了一个状态反馈控制器，以确保快速采样增强 SPSMS 的随机均方可接受性。然后，将结果扩展到存在外部干扰下的 H∞ 性能分析和控制器设计。推导的准则可以转换为基于凸优化的可行问题，并计算奇异扰动参数的上限。此外，提供了一种离散电路系统来验证所提方法的有效性和优越性。