Stabilization for fast sampling discrete-time singularly perturbed singular Markovian systems

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-10-21 DOI:10.1016/j.automatica.2024.111981

Yingqi Zhang , Haoqi Liang , Yuanqing Xia , Jingjing Yan

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引用次数: 0

Abstract

This paper considers the problems of stabilization and

H_{\infty}

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_{\infty}

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.

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快速采样离散时奇异扰动奇异马尔可夫系统的稳定问题

本文探讨了快速采样离散时间奇异扰动奇异马尔可夫系统（SPSMS）的稳定和 H∞ 控制问题。首先引入系统等效方法，将离散快速采样奇异马尔可夫系统模型转化为增强奇异马尔可夫系统模型，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，还提供了一种状态反馈控制器，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扰动时的 H∞ 性能分析和控制器设计。得出的准则可转换为基于凸优化的可行问题，并计算了奇异扰动参数的上界。此外，还提供了一个离散电路系统来验证所提方法的有效性和优越性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.