基于时滞/时滞导数二维分解的时滞系统分析与设计

项目名称： 基于时滞/时滞导数二维分解的时滞系统分析与设计

项目编号： No.61304064

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 曾红兵

作者单位： 湖南工业大学

项目金额： 23万元

中文摘要： 针对时变时滞系统中普遍采用的时滞分解方法存在的局限性，研究更加有效的基于完全时滞分解的时滞区间依赖Lyapunov泛函方法。在此基础上，将完全时滞分解的思想推广应用于处理时滞导数信息，从二维空间的角度，研究时滞/时滞导数二维分解的Lyapunov泛函方法，进一步应用凸组合方法获得时滞相关鲁棒稳定性条件；同时在时滞/时滞导数二维分解的总体框架下，讨论时滞相关鲁棒镇定和鲁棒性能设计问题。基于状态反馈和输出反馈两种情形，建立时滞相关鲁棒稳定性分析、鲁棒镇定和鲁棒性能设计之间的内在联系，寻找时滞相关鲁棒镇定和时滞相关鲁棒性能的条件，研究基于时滞/时滞导数二维分解的时滞相关鲁棒镇定和鲁棒性能设计方法，以及相应的鲁棒镇定控制算法和鲁棒性能综合算法；时滞/时滞导数二维分解方法将有效克服传统方法的局限性和由此带来的保守性。研究结果将为时滞系统分析和设计提供一种有效可行的新方法，在理论上具有重要的科学意义。

中文关键词： 时滞系统；时变时滞；Lyapunov-Krasovskii泛函；积分不等式；

英文摘要： By analyzing the limitations of widely adopted delay-decomposition methods, a complete delay-decomposition approach for constructing delay-interval-dependent Lyapunov functional will be investigated. Furthermore, the idea of the complete delay-decomposition approach will be further extended to handle the information of delay-derivative. As a result, a newly delay/delay-derivative two-dimensional decomposition approach will be proposed to construct Lyapunov functional. In addition, the convex combination method will be applied to obtain delay-dependent stability conditions. Based on the framework of delay/delay-derivative two-dimensional decomposition, the problems of delay-dependent robust stabilization and robust performance design will be discussed. For both state feedback and output feedback control,the relationship among robust stability analysis, robust stabilization and robust performance design will be estabilished. Furthermore, delay-dependent robust stabilization and robust performance conditions will be investigated and the corresponding robust stabilization control and robust performance synthesis algorithms will be presented. The delay/delay-derivative two-dimensional decomposition approach will be able to overcome the limitation of the traditional method and its conservativeness. It is believed that

英文关键词： Tme-delay system；Time-varying delay；Lyapunov-Krasovskii functional；Integral inequality；