基于采样区间分割的线性系统稳定准则  

Stability Criteria of Linear Systems Based on Sampled-Interval Fragmentation Approach

作　　者：练红海 覃事刚[1] 肖伸平[2] 肖会芹[2] LIAN Honghai;QIN Shigang;XIAO Shenping;XIAO Huiqin(School of Wind Energy Engineering,Hunan Electrical College of Technology,Ximgtm 411101;School of Electrical and Information Engineering,Hunan University of Technology,Zhuzhou 412008)

机构地区：[1]湖南电气职业技术学院风能工程学院,湘潭411101 [2]湖南工业大学电气与信息工程学院,株洲412008

出　　处：《系统科学与数学》2021年第2期310-324,共15页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61703153,6167225);湖南省自然科学基金(2018JJ5007,2018JJ5010,2020JJ7023);湖南省教育厅科学研究项目(19C0419,19C0420);湖南电气职院科研基金(2019ZK002,2020ZK001,2020RC001)资助课题。

摘　　要：针对具有网络时延的线性采样控制系统的稳定性问题,基于分割后的采样区间和状态信息,建立了新的双边采样区间依赖闭环Lyapunov泛函.然后,在Lyapunov泛函导数中引入分割后的系统状态方程,并应用2阶Bessel-Legendre不等式和自由矩阵不等式估计泛函导数中的积分项,导出了低保守性的采样控制系统稳定性准则.最后,通过3个例子验证了提出方法的有效性和优越性.The paper aims at the stability of linear sampled-data control systems with network-induced delays.A new two-side sampled-interval-dependent looped Lyapunov functional is established based on the sampled-interval and system state of partition.Then,By introducing system state equation and using 2-order BesselLegendre inequality and free-matrix-based inequality to estimate single integral term in the derivative of Lyapunov functional,some less conservative stability criterion are derived for sampled-data control systems.Finally,two examples are provided to verify the validity and superiority of the proposed methods.

关 键 词：采样控制系统 通信时滞 稳定性 采样区间分割 LYAPUNOV泛函 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]