基于状态分解方法的中立型奇异时滞系统镇定性研究

中立型奇异时滞系统是兼有时滞信息、中立型特性以及奇异特性等因素的一类复杂时滞系统，在模型结构层面更具有一般性且更能有效描述如电力系统、经济系统等实际系统。本项目针对连续时间域上中立型奇异时滞系统，研究基于状态分解方法的镇定性问题。首先分析系统奇异特性、中立型特性以及时滞信息对系统影响，建立系统结构模型，采用状态分解方法，构建状态分解的增广LKF，寻找合适的泛函导数估计方法，借助于积分不等式和自由权矩阵技术，探讨系统正则性与无脉冲性，建立系统时滞相关稳定性条件；在此基础上，构建基于动态输出反馈控制器的系统闭环结构，结合状态分解重组技术，获得等价结构模型，提出控制器设计条件和整定算法；将上述拟建立的方法和结论推广到系统具马尔科夫跳变参数的情形，探讨系统的镇定性问题；提供数值算例或应用实例，检验分析与设计结果有效性与优越性。本项目研究成果将为中立型奇异时滞系统的镇定性问题提供一种新颖有效的方法。

Neutral singular time-delay systems with time-delay information, neutral- and singular- characteristics are a kind of complex time-delay systems. Such systems are more general at the level of model structure and can describe many practical systems effectively such as powers systems and economic systems. This project will investigate the problem of stabilization for neutral singular systems with time-delay based on state decomposition method. First, By analyzing singular characteristics, neutral characteristics, time-delay information and their influences on systems, the models of neutral singular time-delay systems will be established. For the stability problems, how to construct an augmented Lyapunov-Krasovskii functional (LKF) with state decomposition and how to estimate the functional will be investigated. The regularity, non-impulsiveness and stability will be studied via employing integral inequalities and free-weighting matrix techniques. The stability criteria will be obtained. Second, the construction of the closed-loop systems equipped with a dynamic output feedback controller will be established. The equivalent structure models will also be derived based on state decomposition-recombination technology. And the design algorithms for desired dynamic output-feedback controller will be also proposed. Third, the above proposed methods and conclusions are reasonably applied to the considered systems with Markov jump parameters. The stabilization analysis of the systems will be discussed. Finally, numerically examples or real-word examples will be provided to check the effectiveness and advantage of the obtained analysis and design results. The objective of this project is to develop a novel and effective design method for the stabilization of neutral singular time-delay systems.