This paper deals with the stability and positivity analysis of polynomial-fuzzy-model-based (PFMB) control systems with time delay, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop, under imperfect premise matching. To improve the design and realization flexibility, the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions. A sum-of-squares-based stability analysis approach using the Lyapunov stability theory is employed to investigate the positivity and stability of the PFMB control systems and synthesize the polynomial fuzzy controller. In order to relax the stability results, we propose two methods: first, membership functions are considered as symbolic variables in the stability analysis; and second, the property of the membership functions and the boundary information of the membership functions are considered in the stability analysis. A simulation example is given to illustrate the effectiveness of the proposed approach.

中文翻译：

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不完美前提匹配下时滞正多项式模糊模型控制系统的稳定性分析


本文研究了由多项式模糊模型和多项式模糊控制器闭环连接构成的时滞多项式模糊模型（PFMB）控制系统在不完美前提匹配下的稳定性和正性分析。为了提高设计和实现的灵活性，允许多项式模糊模型和多项式模糊控制器有自己的一组前提隶属函数。采用基于李亚普诺夫稳定性理论的平方和稳定性分析方法来研究 PFMB 控制系统的正性和稳定性，并综合多项式模糊控制器。为了放宽稳定性结果，我们提出了两种方法：首先，在稳定性分析中将隶属函数视为符号变量；其次，稳定性分析中考虑了隶属函数的性质和隶属函数的边界信息。给出了一个仿真例子来说明该方法的有效性。