摘要
研究了变周期采样系统的采样区间依赖稳定性问题.采用类Lyapunov泛函方法研究采样系统的稳定性与采样区间的关系,该类Lyapunov泛函不强求正定也不要求连续.通过增加状态与状态导数的交叉项推广了类Lyapunov泛函,然后用新的不等式处理该类Lyapunov泛函的导数,基于类Lyapunov泛函方法导出了采样区间依赖稳定性新结果,然后,在凸多胞型不确定采样系统中推广该结果,得到了鲁棒采样渐近稳定性新准则.最后,用3个仿真例子说明了文章结果比现有的某些结果保守性小.
This paper is concerned with the sampling-interval-dependent stability of sampled-data systems under aperiodic sampling. It adopts Lyapunov-like functional method to investigate the relationship between the stability of sampled-data systems and the sampling-interval. The Lyapunov-like functional is not necessarily positive definite nor continuous. A new Lyapunov-like functional is constructed, which contains the cross term of the state and its derivative. Then by taking advantage of a new inequality to deal with the Lyapunov-like functional derivative, based on the Lyapunov-like functional method, a new result is obtained about the sampling-interval-dependent stability. The result is extended to sampled-data systems under aperiodic sampling with polytopic uncertainty, and a new criterion is derived about the robust stability of the uncertain system. Lastly, three examples show that the proposed results have less conservatism than some existing ones.
作者
冯宗英
邵汉永
邵林
FENG Zongying;SHAO Hanyong;SHAO Lin(Institute of Automation,Qufu Normal University,Rizhao 276826;College of Electronic, Communication and Physics,Shandong University of Science and Technology,Qingdao 266590)
出处
《系统科学与数学》
CSCD
北大核心
2018年第11期1267-1281,共15页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(61374090
61473171)
山东省自然科学杰出青年基金(JQ201515)
山东省泰山学者工程项目(tsqn20161032)资助课题
