离散时滞奇异摄动控制系统的稳定性分析

孙凤琪

doi:10.21656/1000-0887.410208

离散时滞奇异摄动控制系统的稳定性分析

doi: 10.21656/1000-0887.410208

孙凤琪^,

吉林师范大学数学学院, 吉林四平 136000

基金项目:

国家自然科学基金(61741318)

详细信息

作者简介:
孙凤琪（1968—），女，教授，博士，硕士生导师（E-mail: 1092748497@qq.com）.

通讯作者:
孙凤琪（1968—），女，教授，博士，硕士生导师（E-mail: 1092748497@qq.com）.

中图分类号: O231.2
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- 被引次数: 0
出版历程
- 收稿日期: 2020-07-10
- 修回日期: 2020-11-02

Stability Analysis of Discrete Time-Delay Singularly Perturbed Uncertainty Control Systems

SUN Fengqi^,

College of Mathematics, Jilin Normal University, Siping, Jilin 136000, P.R.China

Funds:

The National Natural Science Foundation of China(61741318)

摘要

摘要: 对含不确定性结构的奇异摄动时滞离散控制系统进行稳定性研究.通过设计一种新的LyapunovKrasovskii泛函, 基于Lyapunov稳定性理论，在时滞依赖情形下, 采取交叉项界定技术、线性矩阵分析方法并运用引理, 推出在零到奇异摄动上界的整个区间范围内系统渐近稳定，给出充分性的稳定性判据.之后,再对其进行理论加深和推广, 得到更加简洁性的推论, 可以借助于MATLAB工具箱进行求解.最后，用算例证明本文所得方法的优越性和可行性.
- 稳定性 /
- 离散系统 /
- 时滞依赖 /
- 时滞独立 /
- 交叉项界定法
Abstract: The stability of discrete control systems with time delay, singular perturbation and uncertainty was studied. With a designed new Lyapunov-Krasovskii functional, based on the cross term defined technique, the linear matrix analysis method and the related lemmas, and furthermore, according to the Lyapunov stability theory, the asymptotic stability of the system in the entire interval from zero to the singularly perturbed upper bound was derived in the time-delay-dependent case. Then the sufficient stability criterion was given, which was deepened and generalized to deduce the linearized inferences, and solved with the MATLAB toolbox. The example illustrates the superiority and feasibility of the obtained method.
- stability /
- discrete system /
- delay-dependent /
- delay-independent /
- cross term defined method

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参考文献(16)

康卫, 陈昊, 郝云力. 时滞离散系统的有限时间稳定性分析[J]. 阜阳师范学院学报, 2017,34(3): 1-4.

(KANG Wei, CHEN Hao, HAO Yunli. Finite time stability analysis of discrete time delay systems[J]. Journal of Fuyang Normal University,2017,34(3): 1-4.(in Chinese))

[2]SHANG Wanzhen, ZHANG Xian. Exponential stability analysis of discrete linear time delay systems: method based on weighted discrete orthogonal polynomials[J]. Journal of Natural Science of Heilongjiang University,2017,34(4): 397-403.

[3]贾晓瑞. 时滞饱和离散广义Markov跳变系统的有限时间控制[D]. 硕士学位论文. 秦皇岛: 燕山大学, 2016.(JIA Xiaorui. Finite time control of discrete-time generalized Markov jump systems with time delay saturation[D]. Master Thesis. Qinghuangdao: Yanshan University, 2016.(in Chinese))

[4]朱彪. 几种离散脉冲切换系统的稳定性分析[D]. 硕士学位论文. 株洲: 湖南工业大学, 2014.(ZHU Biao. Stability analysis of several discrete impulsive switched systems[D]. Master Thesis. Zhuzhou: Hunan University of Technology, 2014.(in Chinese))

[5]赵磊, 孙福权, 任俊超, 等. 不确定奇异分布参数系统的鲁棒D稳定[J]. 控制工程, 2018,25(6): 985-992.(ZHAO Lei, SUN Fuquan, REN Junchao, et al. Robust D-stability for singular distributed parameter systems subjected to uncertainties[J]. Control Engineering,2018,25(6): 985-992.(in Chinese))

[6]孙凤琪. 若干类时滞奇异摄动系统的稳定性分析与控制[D]. 博士学位论文. 沈阳: 东北大学, 2012.(SUN Fengqi. Stability analysis and control of several classes of singularly perturbed systems with time delay[D]. PhD Thesis. Shenyang: Northeast University, 2012.(in Chinese))

[7]李笑波. 线性反馈控制驱动下的一类非线性离散系统的渐近稳定性[D]. 硕士学位论文. 南京: 南京师范大学, 2019.(LI Xiaobo. Asymptotic stability of a class of nonlinear discrete systems driven by linear feedback control[D]. Master Thesis. Nanjing: Nanjing Normal University, 2019.(in Chinese))

[8]毛莉, 赵东霞. 双时滞单摆系统的稳定性分析[J]. 云南师范大学学报, 2020,40(2): 38-43.(MAO Li, ZHAO Dongxia. Stability analysis of double delay simple pendulum system[J]. Journal of Yunnan Normal University,2020,40(2): 38-43.(in Chinese))

[9]尹宗明, 张宁, 雷蔓, 等. 一种改进的区间时变时滞系统稳定性准则[J]. 控制工程, 2020,27(3): 462-468.(YIN Zongming, ZHANG Ning, LEI Man, et al. An improved stability criterion for interval time-varying delay systems[J]. Control Engineering,2020,27(3): 462-468.(in Chinese))

[10]SUN P, HUANG Q Z, YANG J X. Diagonal stability analysis of discrete-time nonlinear positive switched systems with delays: a homogeneous polynomial diagonal Lyapunov function method[C]//Proceedings of the 〖STBX〗38th Chinese Control Conference. Guangzhou, China, 2019.

[11]ZHANG T L, DENG F Q, ZHANG W H. Study on stability in probability of general discrete-time stochastic systems[J]. Science China (Information Sciences),2020,63(5): 215-217.

[12]田恩刚, 岳东, 张益军, 等. 改进的含有区间变时滞的离散系统的稳定性分析[C]//自动化学会, 控制理论专业委员会. 第二十七届中国控制会议. 中国, 昆明, 2008.(TIAN Engang, YUE Dong, ZHANG Yijun, et al. Stability analysis of improved discrete-time systems with interval time-varying delay[C]//Control Theory Committee, Society of Automation. Proceedings of the 27th China Control Conference. Kunming, China, 2008.(in Chinese))

[13]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: University of Defense Science and Technology, 2014.(in Chinese))

[14]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))

[15]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, 2019,40(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))

[16]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))

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