This paper proposes a novel Lyapunov stabilization analysis of discrete-time polynomial-fuzzy-model-based control systems with time delay under positivity constraint. The polynomial fuzzy model is constructed to describe the dynamics of a nonlinear discrete-time system with time delay. A model-based polynomial fuzzy controller is designed using nonparallel distributed compensation technique to stabilize the system while driving the system states to positive using the positivity constraints. The Lyapunov stability and positivity conditions are formulated as sum-of squares. To relax the conservativeness of the obtained stability results, two main methods are proposed in this paper: first, the piecewise linear membership functions (PLMFs) are used to introduce the approximate error between piecewise and the original membership functions into the stability analysis; and second, introduce the boundary information of the premise variables into the stability analysis since the premise variables hold rich nonlinearity information. A numerical example is given to demonstrate the effectiveness of the proposed approach.

中文翻译：

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具有时滞和正约束的离散时间多项式模糊系统的基于模型的控制和稳定性分析

本文提出了一种新的基于离散时间多项式模糊模型的控制系统的 Lyapunov 镇定分析，该系统在正性约束下具有时滞。构建多项式模糊模型来描述具有时滞的非线性离散时间系统的动力学。使用非并行分布式补偿技术设计了基于模型的多项式模糊控制器，以稳定系统，同时使用正约束将系统状态驱动为正值。Lyapunov 稳定性和正性条件被公式化为平方和。为了放宽所得稳定性结果的保守性，本文提出了两种主要方法：第一，分段线性隶属函数（PLMF）用于将分段与原始隶属函数之间的近似误差引入稳定性分析中；其次，将前提变量的边界信息引入稳定性分析中，因为前提变量具有丰富的非线性信息。给出了一个数值例子来证明所提出方法的有效性。