摘要
应用新的Lyapunov泛函研究时变时滞系统的渐近稳定性问题.首先,基于Bessel-Legendre积分不等式和改进的自由矩阵积分不等式,提出两个新的时滞乘积型Lyapunov泛函,其充分利用时滞d(t)与二次型函数的乘积信息以及时滞h-d(t)与二次型函数的乘积信息;然后,采用Bessel-Legendre积分不等式和改进的逆凸组合方法估计时滞乘积型Lyapunov泛函导数的积分项,得到两个低保守性的时滞相关稳定性判据;最后,通过两个数值算例进行验证,结果表明,与最近相关方法相比,所提出方法可获得更大的允许时滞上界,进一步表明了所提出方法的可行性和低保守性.
The problem of stability for time-varying delay systems is investigated using a new Lyapunov functional.Two delay-product-type Lyapunov functionals are firstly proposed based on Bessel-Legendre integral inequality and improved free-matrix-based integral inequality.The functional utilizes the information on both the delay d(t)times quadratic function and the delay h-d(t)times quadratic function.Then,by using the Bessel-Legendre integral inequality and the improved reciprocally convex method to estimate the derivative of Lyapunov functional,some less conservative stability criteria are derived for the considered time-varying delay systems.The feasibility and less conservativeness of the obtained criteria are verified by two numerical examples.The results obtained show that the proposed methods can provide a larger admissible delay upper bounds than some existing ones.
作者
练红海
肖伸平
陈刚
张晓虎
邓鹏
LIAN Hong-hai;XIAO Shen-ping;CHEN Gang;ZHANG Xiao-hu;DENG Peng(School of Electrical and Information Engineering,Hunan University of Technology,Zhuzhou 412008,China;School of Wind Energy Engineering,Hunan Electrical College of Technolog,Xiangtan 411101,China;Key Laboratory for Control and Intelligent Equipment of Hunan Province,Zhuzhou 412008,China)
出处
《控制与决策》
EI
CSCD
北大核心
2020年第4期1017-1024,共8页
Control and Decision
基金
国家自然科学基金项目(61672225)
湖南省自然科学基金项目(2017JJ4021,2018JJ4075)
湖南电气职业技术学院自然科学基金重点项目(2018ZK001).
作者简介
练红海(1990-),男,硕士,从事鲁棒控制、采样控制、网络控制的研究,E-mail:1132830550@qq.com;通讯作者:肖伸平(1965-),男,教授,博士生导师,从事鲁棒控制、过程控制、智能控制、电力系统稳定性等研究,E-mail:xsph_519@163.com;陈刚(1977-),男,副教授,从事鲁棒控制、时滞控制和网络控制等研究,E-mail:chengang@hut.edu.cn;张晓虎(1978-),男,讲师,从事智能控制、优化控制等研究,E-mail:zxh1252@163.com;邓鹏(1985-),男,讲师,从事时滞控制、采样控制和网络控制等研究,E-mail:253402957@qq.com.
