This paper is concerned with the fuzzy-model-based nonfragile control problem for discrete-time nonlinear singularly perturbed systems with stochastic jumping parameters. The stochastic parameters are generated from the semi-Markov process. The memory property of the transition probabilities among subsystems is fully considered in the investigated systems. Consequently, the restriction that the transition probabilities are memoryless in widely used discrete-time Markov jump model can be removed. Based on the T-S fuzzy model approach and semi-Markov kernel concept, several criteria ensuring $\delta$-error mean square stability of the underlying closed-loop system are established. With the help of those criteria, the designed procedures which could well deal with the fragility problem in the implementation of the proposed fuzzy-model-based controller are presented. A technique is developed to estimate the permissible maximum value of singularly perturbed parameter for discrete-time nonlinear semi-Markov jump singularly perturbed systems. Finally, the validity of the established theoretical results is illustrated by a numerical example and a modified tunnel diode circuit model.

中文翻译：

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具有半马尔可夫跳跃参数的非线性奇异摄动系统的基于模糊模型的非脆弱控制

本文涉及具有随机跳跃参数的离散时间非线性奇异摄动系统的基于模糊模型的非脆弱控制问题。随机参数由半马尔可夫过程生成。所研究的系统充分考虑了子系统间转移概率的记忆特性。因此，可以消除广泛使用的离散时间马尔可夫跳跃模型中转移概率无记忆的限制。基于TS模糊模型方法和半马尔可夫核概念，建立了保证底层闭环系统$\delta$-误差均方稳定性的几个标准。在这些标准的帮助下，设计的程序可以很好地处理所提出的基于模糊模型的控制器的实现中的脆弱性问题。开发了一种技术来估计离散时间非线性半马尔可夫跳跃奇异摄动系统的奇异摄动参数的允许最大值。最后，通过数值例子和修改后的隧道二极管电路模型说明了所建立的理论结果的有效性。