离散区间二型T-S模糊时滞系统的吸引域估计及局部控制

In modeling domains, nonlinearity and uncertainty can be effectively handled by interval type-2 T-S fuzzy model. However, the existing literature focuses on the global stability of interval type-2 T-S fuzzy model, and the influence of the modeling domains is not considered. Thus, the global fuzzy controller cannot always stabilize the original nonlinear systems. The augmented Lyapunov-Krasovskii functional which contains the information of the first and second order differences of delay variables, are constructed by considering the delay change information. The local stability analysis, local state feedback control, local tracking control, and observer-based local control for discrete interval type-2 T-S fuzzy time-delay systems are investigated by using the augmented Lyapunov-Krasovskii functional and considering the shape information of upper and lower membership functions, and thus less conservative results can be obtained. Using Lyapunov level set method, the estimation of region of attraction is developed in the form of linear matrix inequality. In order to enhance the degree of freedom, the premise membership functions and the number of rules of the proposed controller and observer are different from those of the discrete interval type-2 T-S fuzzy systems with time-delay. The objective of this project is to make a breakthrough for the local control of discrete interval type-2 T-S fuzzy systems with time-delay and to provide new approaches and theoretical foundation for the analysis and synthesis of the nonlinear systems subject to parameter uncertainties and time-delay.

区间二型T-S模糊模型在建模域内能很好地处理系统中的非线性和不确定性。现有文献主要关注区间二型T-S模糊模型的全局稳定性，而忽略了建模域的影响，以致设计的全局模糊控制器不能总是镇定原始的非线性系统。本项目针对离散区间二型T-S模糊时滞系统，充分考虑时滞变化信息，构造含有时滞变量一阶差分及二阶差分信息的增广李雅普诺夫-克拉索夫斯基泛函。利用上、下隶属函数的形状信息和构造的增广李雅普诺夫-克拉索夫斯基泛函，提出较少保守性的局部稳定性分析、状态反馈控制、跟踪控制以及基于观测器的局部控制方法。利用李雅普诺夫水平集法，提出基于线性矩阵不等式的吸引域估计。为了增强设计的自由度，提出的控制器和观测器不必与离散区间二型T-S模糊时滞系统分享相同的前提隶属函数和规则个数。本项目旨在对离散区间二型T-S模糊时滞系统的局部控制有所突破，以期为具有参数不确定非线性时滞系统的分析和综合提供新的方法和理论依据。

区间二型T-S模糊模型在建模域内能很好地处理系统中的非线性和不确定性，已经被广泛地用来处理参数不确定非线性系统。本项目充分考虑时滞变化信息和状态信息，构造了包含更多时滞和状态信息的增广Lyapunov–Krasovskii泛函，获得了较少保守性的时滞依赖条件。充分考虑隶属函数的界信息，提出了不增加松弛变量的隶属函数依赖分析方法。结合辅助矩阵和不增加松弛变量的隶属函数依赖分析方法，发展了新型参数依赖Lyapunov–Krasovskii泛函，消除了Lyapunov矩阵必须为正定的限制条件。提出了双重求和不等式的新型放缩方法，可以广泛应用于离散线性时滞系统，一型T-S模糊时滞系统和区间二型模糊时滞系统，解决了基于三重求和项的Lyapunov–Krasovskii泛函推导较少保守性的线性矩阵不等式条件的难题。通过Lyapunov水平集，提出了区间二型T-S模糊时滞系统的的局部控制和吸引域估计方法，提出的条件可以表示为线性矩阵不等式，并保证估计的吸引域包含在建模域内。通过本项目的实施，为非线性时滞系统的分析和综合提供了新的方法，具有重要意义。