基于状态分解的离散奇异时滞系统的容许性和$H_{\infty}$性能分析

doi:10.12341/jssms22181

系统科学与数学 ›› 2023, Vol. 43 ›› Issue (2): 271-280.DOI: 10.12341/jssms22181

• • 下一篇

基于状态分解的离散奇异时滞系统的容许性和$H_{\infty}$性能分析

黎书杰¹, 智亚丽^1,2, 孙承宇¹, 孙先涛¹

1. 安徽大学电气工程与自动化学院, 合肥 230601;
2. 计算智能与信号处理教育部重点实验室, 合肥 230601

收稿日期:2022-03-18 修回日期:2022-08-21 出版日期:2023-02-25 发布日期:2023-03-16
通讯作者: 智亚丽,Email:zhiyali87828@163.com
基金资助:
国家自然科学基金(62103001),安徽省教育厅高校自然科学重点研究项目(K120437022)资助课题.

PDF ( 5 ) 引用

黎书杰,智亚丽,孙承宇,孙先涛. 基于状态分解的离散奇异时滞系统的容许性和$H_{\infty}$性能分析[J]. 系统科学与数学, 2023, 43(2): 271-280.

LI Shujie, ZHI Yali, SUN Chengyu, SUN Xiantao. Admissibility and $H_{\infty}$ Performance Analysis of Discrete-Time Singular Systems with Time Delays Based on the State Decomposition[J]. Journal of Systems Science and Mathematical Sciences, 2023, 43(2): 271-280.

Admissibility and $H_{\infty}$ Performance Analysis of Discrete-Time Singular Systems with Time Delays Based on the State Decomposition

LI Shujie¹, ZHI Yali^1,2, SUN Chengyu¹, SUN Xiantao¹

1. School of Electrical Engineering and Automation, Anhui University, Hefei 230601;
2. Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Hefei 230601

Received:2022-03-18 Revised:2022-08-21 Online:2023-02-25 Published:2023-03-16

针对一类具有外部扰动的离散奇异时滞系统,文章通过建立系统的微分-代数方程,研究其容许性及$H_{\infty}$性能分析问题.为此,首先利用状态分解方法构造一个在二次型和二重积分二次型中都只含有部分状态量以及相关项的Lyapunov函数.其次,利用求和不等式,自由权矩阵方法等技术对函数的前向差分进行估计,建立一个使系统满足一定$H_{\infty}$性能水平的容许性分析条件.该条件既能实现降低保守性的目的,又能尽可能地减少计算量.最后,通过数值实例验证所提方法的有效性和优越性.

关键词： 离散奇异时滞系统, 状态分解, 容许性, $H_{\infty}$ 性能

This paper is concerned with the problem of admissibility and $H_{\infty}$ for discrete-time singular systems with time delays. Firstly, by decomposing the considered systems to differential-algebraic equations, the state decomposition method for continuous-time singular systems with time delays is expanded to discrete-time singular systems with time delays. The purpose is to construct a special Lyapunov functional whose the (double integral) quadratic forms are just composed of partial states and their related items. Then, the forward difference of the constructed Lyapunov functional is estimated by utilizing the summation inequality and the free matrix weighting approach, and thus a sufficient condition that can guarantee the considered systems with $H_{\infty}$ performance to be admissible is obtained. This condition has less conservatism and less computational burden, which is finally demonstrated by some numerical examples.

Key words: Discrete-time singular systems with time delays, state decomposition, admissibility, $H_{\infty}$ performance

MR(2010)主题分类:

93E15

分享此文:

[1] Xu S, Dooren P V, Stefan R, et al. Robust stability and stabilization for singular delay systems with state delay and parameter uncertainty. IEEE Trans. Autom. Control, 2002, 47(7): 1122- 1128.
[2] Fridman E. Stability of linear descriptor systems with delay: A Lyapunov-based approach. J. Math. Analys. Appl., 2002, 273(1): 24-44.
[3] He Y, Wang Q G, Xie L, et al. Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Trans. Autom. Control, 2007, 52(2): 293-299.
[4] Liu Z Y, Lin C, Chen B. A neutral system approach to stability of singular time-delay systems. J. Franklin Inst., 2014, 351(10): 4939-4948.
[5] Liu G. New results on stability analysis of singular time-delay systems. Int. J. Syst. Sci., 2017, 48(7): 1395-1403.
[6] Li W, He Z, Sun W, et al. Admissibility analysis for Takagi-Sugeno fuzzy singular systems with time delay. Neurocomputing, 2016, 205: 336-340.
[7] Liu Z Y, Lin C, Chen B. Admissibility analysis for linear singular systems with time-varying delays via neutral system approach. ISA Trans., 2016, 61: 141-146.
[8] Zhi Y L, He Y, Shen J, et al. New stability criteria of singular systems with time-varying delay via free-matrix-based integral inequality. Int. J. Syst. Sci., 2018, 49(5): 1032-1039.
[9] Luu T H, Nam P T. Stability analysis of singular time-delay systems using the auxiliary functionbased double integral inequalities. Int. J. Syst. Sci., 2021, 52(9): 1868-1881.
[10] Zhi Y L, He Y, Wu M, et al. Dissipativity analysis of singular time-delay systems via state decomposition method. IEEE Trans. Syst., Man, Cyber. Syst., 2020, 50: 3936-3942.
[11] Zhi Y L, He Y, Wu M, et al. New results on dissipativity analysis of singular systems with time-varying delay. Inf. Sci., 2019, 479: 292-300.
[12] Tian Y, Wang Z. Exponential admissibility analysis for singular systems with time-varying delay based on a parameter-dependent reciprocally convex inequality, Int. J. Syst. Sci., 2020, 51(16): 3199-3212.
[13] Li Y, He Y. New insight into admissibility analysis for singular systems with time-varying delays, Int. J. Syst. Sci., 2020, 52(13): 2752-2762.
[14] Chen W, Gao F, She J, et al. Further results on delay-dependent stability for neutral singular systems via state decomposition method. Chaos, Soli. Frac., 2020, 141: 110408.
[15] Zhao Y, Ma Y. Asynchronous H∞ control for hidden singular Markov jump systems with incomplete transition probabilities via state decomposition approach. Appl. Math. Comput., 2021, 407(17): 126304.
[16] Du Z P, Zhang Q L, Liu L L. New delay-dependent robust stability of discrete singular systems with time-varying delay. Asian J. Control, 2011, 13(1): 136-147.
[17] Feng Z G, Lam J, Gao H J. Delay-dependent robust H∞ controller synthesis for discrete singular delay systems. Int. J. Robust Non. Control, 2011, 21(16): 1880-1902.
[18] Zhang X, Zhu H Y. Robust stability and stabilization criteria for discrete singular time-delay LPV systems. Asian J. Control, 2012, 14(4): 1084-1094.
[19] Shao Y, Liu X, Sun X, et al. A delay decomposition approach to H∞ admissibility for discretetime singular delay systems. Inf. Sci., 2014, 279: 893-905.
[20] Wan X, Wu M, He Y. Stability analysis for discrete time-delay systems based on new finite-sum inequalities. Inf. Sci., 2016, 369: 119-127.
[21] Boyd S, Ghaoui L E, Feron E, et al. Linear Matrix Inequality in System and Control. Philadelphia: SIAM Studies in Applied Mathematics, 1994.
[22] Feng Z, Zhang H, Lam H. New results on dissipative control for a class of singular Takagi-Sugeno fuzzy systems with time delay. IEEE Trans. Fuzzy Syst., 2022, 30(7): 2466-2475.

[1]	周在莹. 矩阵损失函数下回归系数矩阵的非齐次线性估计的可容许性[J]. 系统科学与数学, 2010, 30(12): 1597-1605.
[2]	刘刚;张尚立. 一般增长曲线模型回归系数线性估计的可容许性[J]. 系统科学与数学, 2009, 29(3): 315-322.
[3]	王志忠;康新梅;刘锋. 误差方差的非齐次估计的可容许的充要条件[J]. 系统科学与数学, 2006, 26(6): 709-713.
[4]	程正东;陈桂景. 多元线性模型中的有偏估计[J]. 系统科学与数学, 2004, 24(4): 504-512.
[5]	黄言军;赖民;宋立新. Pitman准则下指数分布刻度参数幂的分组定数截尾估计[J]. 系统科学与数学, 2000, 20(1): 24-030.
[6]	魏凤荣. 具有特殊协方差结构的SURE模型中参数估计的若干结果[J]. 系统科学与数学, 1999, 19(1): 86-094.
[7]	林举干;孙孝前. 二次约束下多指标线性模型回归系数线性估计的可容许性[J]. 系统科学与数学, 1997, 17(1): 66-072.
[8]	鹿长余;沙秋英;李维新. 方差分量的非负二次同时估计的可容许性[J]. 系统科学与数学, 1996, 16(4): 361-366.

阅读次数

全文

摘要