基于状态分解的离散奇异时滞系统的容许性和H_(∞)性能分析  

Admissibility and H∞Performance Analysis of Discrete-Time Singular Systems with Time Delays Based on the State Decomposition

作　　者：黎书杰 智亚丽 孙承宇 孙先涛 LI Shujie;ZHI Yali;SUN Chengyu;SUN Xiantao(School of Electrical Engineering and Automation,Anhui University,Hefei 230601;Key Laboratory of Intelligent Computing and Signal Processing,Ministry of Education,Hefei 230601)

机构地区：[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

出　　处：《系统科学与数学》2023年第2期271-280,共10页Journal of Systems Science and Mathematical Sciences

基　　金：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。

摘　　要：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∞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∞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.This paper is concerned with the problem of admissibility and H∞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∞performance to be admissible is obtained.This condition has less conservatism and less computational burden,which is finally demonstrated by some numerical examples.

关 键 词：离散奇异时滞系统 状态分解 容许性 H_(∞)性能 

分 类 号：O175[理学—数学]