This article mainly addresses the stabilization issue of discrete-time interval type-2 fuzzy (IT-2F) semi-Markov jump systems in the presence of denial-of-service attacks by means of homogeneous polynomial approach. By employing the IT-2F technique, nonlinear features, such as possible uncertainties and unknown perturbations, are effectively expressed, and the corresponding membership functions of the fuzzy rules facilitate the application of subsequent polynomial method. A homogeneous polynomially parameter-dependent (HPPD) control law and a type of homogeneous polynomial-based fuzzy functions are designed for enlarging feasible parameter space as well as reducing the conservatism of the conditions, which are both HPPD on membership functions. Moreover, the conclusions concerning nonpolynomial controller and partial unavailable semi-Markov kernel are covered. It is also exemplified that the larger the degree of polynomial matrices, the less energy consumed by the controller. Finally, two examples of quarter-car suspension model and tunnel diode circuit model are provided to support the effectiveness of the presented results.

中文翻译：

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具有 DoS 攻击的区间 2 型模糊半马尔可夫跳跃系统的松弛稳定：齐次多项式方法


本文主要通过齐次多项式方法解决存在拒绝服务攻击时离散时间间隔2型模糊（IT-2F）半马尔可夫跳跃系统的稳定性问题。采用IT-2F技术，有效地表达了可能的不确定性和未知扰动等非线性特征，并且相应的模糊规则隶属函数便于后续多项式方法的应用。为了扩大可行参数空间并降低条件的保守性，设计了齐次多项式参数相关（HPPD）控制律和一类基于齐次多项式的模糊函数，它们都是隶属函数上的HPPD。此外，还涵盖了有关非多项式控制器和部分不可用半马尔可夫核的结论。还举例说明了多项式矩阵的次数越大，控制器消耗的能量越少。最后，提供了四分之一汽车悬架模型和隧道二极管电路模型的两个例子来支持所提出结果的有效性。