SUN Fengqi. Stability Analysis of Uncertain Singularly Perturbed Filter Error Dynamic Systems With Time Delays[J]. Applied Mathematics and Mechanics, 2020, 41(8): 899-911. doi: 10.21656/1000-0887.400368
 Citation: SUN Fengqi. Stability Analysis of Uncertain Singularly Perturbed Filter Error Dynamic Systems With Time Delays[J]. Applied Mathematics and Mechanics, 2020, 41(8): 899-911.

# Stability Analysis of Uncertain Singularly Perturbed Filter Error Dynamic Systems With Time Delays

##### doi: 10.21656/1000-0887.400368
Funds:  The National Natural Science Foundation of China(61741318)
• Rev Recd Date: 2020-06-17
• Publish Date: 2020-08-01
• With the Lyapunov stability theory, the linear matrix inequality method, the time delay piecewise analysis method, the matrix analysis method and the free weight matrix method, the stability of singularly perturbed filter error dynamic systems with time-varying delays and uncertain structures was studied on the basis of the previous filter design theory. Through construction of a new Lyapunov function, with a new cross-term definition method and according to the system characteristics, a new criterion for stability of filter error dynamic systems in 2 cases of time delay dependence and time delay independence was derived. Finally, the selected numerical example illustrates the effectiveness and feasibility of the obtained results.
•  [1] 孙凤琪. 不确定性时滞奇异摄动控制系统的滤波器设计[J]. 控制工程, 2020,27(8): 102-103.(SUN Fengqi. Filter design of singular perturbation control system with uncertain time-delay[J]. Control Engineering,2020,27(8): 102-103.(in Chinese)) [2] 孙凤琪. 若干类时滞奇异摄动系统的稳定性分析与控制[M]. 北京: 科学出版社, 2018.(SUN Fengqi. Stability Analysis and Control of Several Kinds of Singularly Perturbed Systems With Delays [M]. Beijing: Science Press, 2018.(in Chinese)) [3] 徐赵文. 复杂受限系统的控制与滤波理论研究[D]. 博士学位论文. 杭州: 浙江大学, 2018. （XU Zhaowen. Research on control and filtering theory of complex constrained systems[D]. PhD Thesis. Hangzhou: Zhejiang University, 2018.(in Chinese)) [4] 陈进. 不确定系统有限时间鲁棒滤波问题的研究[D]. 硕士学位论文. 哈尔滨: 哈尔滨工业大学, 2017.(CHEN Jin. Research on finite-time robust filtering for uncertain systems[J]. Master Thesis. Harbin: Harbin Institute of Technology, 2017.(in Chinese)) [5] 王亚龙. 基于LMI的变时滞系统鲁棒H∞ 滤波及应用[D]. 硕士学位论文. 哈尔滨: 哈尔滨工业大学, 2015.(WANG Yalong. Robust H∞ filtering for time-varying delay systems based on LMI and its application[D]. Master Thesis. Harbin: Harbin Institute of Technology, 2015.(in Chinese)) [6] 李峰. Markov切换系统的有限时间约束控制与滤波[D]. 硕士学位论文. 马鞍山: 安徽工业大学, 2017.(LI Feng. Limited-time constrained control and filtering for Markov switched systems[D]. Master Thesis. Maanshan: Anhui University of Technology, 2017.(in Chinese)) [7] 郑重. 参数切换重复标量非线性系统的控制与滤波研究[D]. 博士学位论文. 哈尔滨: 哈尔滨工业大学, 2017.(ZHENG Zhong. Study on control and filtering of repetitive scalar nonlinear systems with parameter switching[D]. PhD Thesis. Harbin: Harbin Institute of Technology, 2017.(in Chinese)) [8] 肖小庆. 线性切换系统：事件触发控制、滤波与广义动态分析[D]. 博士学位论文. 南京: 南京理工大学, 2017.(XIAO Xiaoqing. Linear switching system: event triggering control, filtering and generalized dynamic analysis[D]. PhD Thesis. Nanjing: Nanjing University of Science and Technology, 2017.(in Chinese)) [9] 侯男. 几类系统非脆性滤波方法研究[D]. 硕士学位论文. 大庆: 东北石油大学, 2015.(HOU Nan. Research on non-brittle filtering methods for several systems[D]. Master Thesis. Daqing: Northeast Petroleum University, 2015.(in Chinese)) [10] 张舒. 非线性系统的鲁棒滤波及控制方法研究[D]. 硕士学位论文. 大庆: 东北石油大学, 2015.(ZHANG Shu. Study on robust filtering and control method of nonlinear systems [D]. Master Thesis. Daqing: Northeast Petroleum University, 2015.(in Chinese)) [11] 张琦. T-S非线性模糊网络控制系统鲁棒控制及滤波[D]. 硕士学位论文. 大庆: 东北石油大学, 2017.(ZHANG Qi. T-S nonlinear fuzzy networked control system robust control and filtering[D]. Master Thesis. Daqing: Northeast Petroleum University, 2017.(in Chinese)) [12] 成军. 几类跳变系统的有限时间稳定性分析与控制问题研究[D]. 博士学位论文. 成都: 电子科技大学, 2015.(CHENG Jun. Finite-time stability analysis and control of several jump systems[D]. PhD Thesis. Chengdu: University of Electronic Science and Technology of China, 2015.(in Chinese)) [13] 周秀杰. 网络控制系统的鲁棒控制及滤波研究[D]. 硕士学位论文. 大庆: 东北石油大学, 2015.(ZHOU Xiujie. Robust control and filtering of networked control systems[D]. Master Thesis. Daqing: Northeast Petroleum University, 2015.(in Chinese)) [14] 陈照辉. 时滞系统稳定控制与滤波及其应用研究[D]. 博士学位论文. 成都: 电子科技大学, 2015.(CHEN Zhaohui. Stability control and filtering of time-delay systems and their applications[D]. PhD Thesis. Chengdu: University of Electronic Science and Technology of China, 2015.(in Chinese)) [15] 冯波. 线性滤波估计算法研究及在惯性导航系统中的应用[D]. 博士学位论文. 北京: 北京理工大学, 2014.(FENG Bo. Research on linear filter estimation algorithm and its application in inertial navigation system[D]. PhD Thesis. Beijing: Beijing University of Technology, 2014.(in Chinese)) [16] 曹璐. 基于最小模型误差准则的非线性滤波及控制理论与应用研究[D]. 博士学位论文. 长沙: 国防科学技术大学, 2014.(CAO Lu. Theory and application of nonlinear filtering and control based on minimum model error criterion[D]. PhD Thesis. Changsha: National University of Defense Technology, 2014.(in Chinese)) [17] 戴德宣, 王少伟. 趋旋性微生物在幂律流体饱和水平多孔层中的热-生物对流稳定性分析[J]. 应用数学和力学, 2019,40(8): 856-865.(DAI Dexuan, WANG Shaowei. Linear stability analysis on thermo-bioconvection of gyrotactic microorganisms in a horizontal porous layer saturated by a power law fluid[J]. Applied Mathematics and Mechanics,2019,40(8): 856-865.(in Chinese)) [18] 芦泽阳, 李树江, 王向东. 采用RBF网络的喷雾机喷杆自适应动态面跟踪控制[J]. 应用数学和力学, 2019,〖STHZ〗 40(7): 801-809.(LU Zeyang, LI Shujiang, WANG Xiangdong. Adaptive RBF-network dynamic surface tracking control of sprayer boom systems[J]. Applied Mathematics and Mechanics,2019,40(7): 801-809.(in Chinese)) [19] 赵晨, 戈新生. 基于虚拟完整约束的欠驱动起重机控制方法[J]. 应用数学和力学, 2019,40(3): 302-310.(ZHAO Chen, GE Xinsheng. A control method for underactuated cranes based on virtual holonomic constraints[J]. Applied Mathematics and Mechanics,2019,40(3): 302-310.(in Chinese))

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142