中立型多时滞系统的稳定性分析与控制综合

Time-delay system of neutral type is a kind of system with delays in both the state and the derivative of the state. Such systems have extensive applications in engineering areas such as energy systems, communication and power systems. This project will study time-delay systems of neutral type with multiple delays. Based on complex frequency domain analysis, the necessary and sufficient stability conditions of the associated difference equations will be studied. By using of the completed quadratic Lyapunov-Krasovskii method, discretized Lyapunov functions and SOS approaches, the stability of time-delay systems of neutral type with multiple delays will be studied. The more exact maximun of time delay will be obtained and the efficient method to reduce the complexity will be found. On the base of functional analysis, the inverse operator of the infinite dimension operator will be constructed, and the controller will be designed. Numerical examples or real-word examples will be provided to check the advantage and effectiveness of the obtained analysis and design results. This project aims to obtain a systematic class of theoretical results and to improve the control theory of time-delay systems of neutral type.

中立型时滞系统是一类系统的状态和状态的导数项中均含有时滞的系统，在能源系统、通信电力等实际工程领域具有广泛的应用。本项目拟针对具有多重时滞的中立型系统，基于复频域分析方法，研究其附属差分方程达到指数稳定的充分必要条件；基于完全二次Lyapunov-Krasovskii泛函方法，利用离散化Lyapunov函数法和SOS多项式法，分析中立型多时滞系统的稳定性，获得更精确的时滞上界的同时减小计算复杂度；利用泛函分析理论，分析无穷维算子的可逆性，构造出其逆算子，完成基于完全二次L-K泛函的控制器设计；提供数值算例或应用实例，检验分析与设计结果的先进性和有效性。本项目旨在形成系统的理论研究成果，改进和发展中立型时滞系统的稳定性分析与综合控制理论。

中立型时滞系统具有重要的研究价值和广泛应用。本项目针对中立型时滞系统，基于Lyapunov-Krasovskii泛函方法，分析了中立型时滞系统的稳定性与控制问题，提出了随机中立型时滞系统的依赖于衰减率的稳定性条件，获得了中立型时滞系统的具有较低保守性的状态估计判据，设计了基于采样数据的中立型时滞系统的事件触发控制器。并进一步研究了非线性时滞系统的输出反馈采样控制、事件触发实际跟踪、输出调节控制等，提出了新的分析与设计方法，得到了一系列较成体系的研究成果。