考虑通信时滞的采样控制系统稳定性分析  

Stability analysis for sampled-data control systems by considering communication delay

作　　者：陈刚[1,2] 刘博林 陈云 邓琪 王震 CHEN Gang;LIU Bolin;CHEN Yun;DENG Qi;WANG Zheng(College of Electrical and Information Engineering,Hunan University of Technology,Zhuzhou 412007,China;College of Railway Transportation,Hunan University of Technology,Zhuzhou 412007,China;State Key Laboratory of Synthetical Automation for Process Industries,Northeastern University,Shenyang 110819,China)

机构地区：[1]湖南工业大学电气与信息工程学院,湖南株洲412007 [2]湖南工业大学轨道交通学院,湖南株洲412007 [3]东北大学流程工业综合自动化国家重点实验室,辽宁沈阳110819

出　　处：《中南大学学报（自然科学版）》2024年第3期963-972,共10页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(62173136)。

摘　　要：为了研究带有通信时滞的采样控制系统的稳定性问题,首先,考虑采样区间的采样特性,构造一种依赖于采样区间最值的闭环泛函,在这种泛函中,泛函相关的矩阵不需要满足正定定义,且矩阵随着采样区间最值的变化而变化;然后,利用采样控制系统的动态信息以及定积分的分部积分法,提出一些含自由矩阵的零等式;再次,结合广义自由矩阵积分不等式,推导出采样控制系统带有通信时滞和无通信时滞的2个稳定性判据;最后,通过数值和实际仿真验证采样区间最值的闭环泛函方法的可靠性。研究结果表明:基于采样区间最值的双边闭环泛函能够使采样控制系统稳定性判断更优且更有效。The stability problem of sampled-data control systems with communication delay was investigated.Firstly,a looped functional that depends on the maximum value of the sampling interval was constructed by considering the sampling characteristics of the sampling interval.The matrices associated with the functional do not need to satisfy the positive definition varing with the maximum value of the sampling interval.Secondly,using the dynamic information of the sampled-data control system and the integration by parts of a definite integral,some zero equations containing free matrices were proposed.Thirdly,combined with the generalized free-matrix based integral inequality,the stability criterion for the time-delay sampling control system and the stability criterion for the sampling control system without time delay were deduced.Finally,the reliability of the closed loop functional method with the maximum value of sampling interval was verified by numerical and practical simulation.The results show that the two-sided closed-loop functional based on the maximum value of the sampling interval can make the stability criterion of the sampling control system more optimal and effective.

关 键 词：采样控制系统 稳定性分析 时滞 LYAPUNOV-KRASOVSKII泛函 闭环泛函 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]