线性时滞系统的稳定性分析与控制  

Stability Analysis and Control of Linear Systems with Time-Delay

作　　者：刘蕾[1] 罗宾[1] 韩存武[1] 孙德辉[1] 

机构地区：[1]北方工业大学现场总线及自动化北京市重点实验室,北京100144

出　　处：《计算机仿真》2015年第8期327-331,共5页Computer Simulation

基　　金：国家自然科学基金(61174116);北京市自然科学基金(4142014)

摘　　要：研究带有状态时滞的线性系统时滞相关稳定性分析与状态反馈控制器设计问题。通过构造新的Lyapunov-Krasovskii泛函,基于线性矩阵不等式给出了系统渐近稳定的充分条件。然后,依据所得的稳定性充分条件,分别提出无记忆和有记忆状态反馈控制器的设计方法。由于在推导过程中没有使用不等式变换的方法,使得结果具有较小的保守性。最后,通过对不同对象、不同参数的时滞系统进行数值仿真,以及对不同时滞上界情况进行状态曲线分析,并与已有方法进行比较,说明文中结论具有较小的保守性,以及所提方法的有效性和正确性。The delay- dependent stability analysis and state feedback controller design problems for linear sys- tems with state delay are considered. Firstly, based on linear matrix inequality a new Lyapunov - Krasovskii function is constructed and a sufficient condition for the asymptotically stability of system is presented. Secondly, the methods of memory- less and memorial state feedback controllers are designed according to the sufficient condition. The inequalities＇ transformation, which often leads to conservatism, is not required for delay - dependent results. Finally, the time- delay systems with different parameters are simulated, and the state curves under different delay bounds are also analyzed carefully, which are provided to demonstrate the reduced conservatism and effectiveness and cor- rectness of the proposed results.

关 键 词：线性系统 时滞依赖 稳定性 状态反馈 线性矩阵不等式 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]