不确定随机奇异时变时滞马尔可夫跳变系统的有限时间保性能H∞控制  

Finite-time Guaranteed Cost H∞Control for Uncertain Stochastic Singular Markov Jump Systems with Time-varying Delays

作　　者：徐放 王天成 XU Fang;WANG Tiancheng(School of Mathematics and Statistics Science,Ludong University,Yantai 264039,China)

机构地区：[1]鲁东大学数学与统计科学学院,山东烟台264039

出　　处：《鲁东大学学报(自然科学版)》2025年第1期72-82,共11页Journal of Ludong University:Natural Science Edition

基　　金：国家自然科学基金(62373179)。

摘　　要：本文针对一类带有马尔可夫切换模式的不确定随机奇异时变时滞系统,提出了系统解的正则无脉冲条件,通过构造随机Lyapunov-Krasovskii泛函,应用广义It8公式、Moore-Penrose逆公式、Dunkin公式以及Bellman-Gronwall引理,以严格线性矩阵不等式的形式获得了使闭环系统有限时间鲁棒随机有界的充分条件,同时设计了有限时间保性能H∞控制器。最后,通过数值算例验证了设计方案的有效性。This paper addresses a class of uncertain stochastic singular time-varying delay systems with Markov switching.The regularity and impulse-free conditions are proposed for solution of the system.By constructing a stochastic Lyapunov-Krasovskii functional and applying generalized It formula,the Moore-Penrose inverse formula,Dunkin formula,and the Bellman-Gronwall lemma,sufficient conditions for the finite-time robust stochastic boundedness of the closed-loop system are obtained in the form of strict linear matrix inequalities.Additionally,a finite-time guaranteed cost H∞controller was designed.Finally,the effectiveness of the proposed design scheme was verified through the numerical example.

关 键 词：有限时间保性能H_∞控制 随机奇异系统 马尔可夫跳变系统 时变时滞 线性矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]