具有半马尔可夫跳跃的时变时滞系统的滑模控制研究

数学物理学报 ›› 2023, Vol. 43 ›› Issue (2): 549-562.

具有半马尔可夫跳跃的时变时滞系统的滑模控制研究

付亲宏(),熊良林^*(),张海洋,秦娅,权沈爱

云南民族大学数学与计算机科学学院昆明 650500

收稿日期:2022-01-29 修回日期:2022-10-17 出版日期:2023-04-26 发布日期:2023-04-17
通讯作者: 熊良林，E-mail: lianglin_5318@126.com
作者简介:付亲宏，E-mail: 2435650934@qq.com
基金资助:
国家自然科学基金(12061088)

Sliding Mode Control for Time-Varying Delay Systems with Semi-Markov Jump

Fu Qinhong(),Xiong Lianglin(),Zhang Haiyang,Qin Ya,Quan Shenai

School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500

Received:2022-01-29 Revised:2022-10-17 Online:2023-04-26 Published:2023-04-17
Supported by:
NSFC(12061088)

摘要/Abstract

摘要：

该文研究具有半马尔可夫跳跃的不确定连续时变时滞系统的滑模控制器设计问题. 首先, 通过研究系统的动力学特性, 结合滑模面, 建立描述滑模完整动力学的奇异系统. 然后, 充分考虑时滞信息, 构造符合系统特性的 Lyapunov 泛函, 给出滑模面存在的充分条件, 保证滑模动力学系统的随机稳定性. 基于此, 设计滑模控制器, 使闭环系统最终收敛到滑模面. 最后, 通过一个数值算例验证该文方法的有效性.

关键词: 半马尔可夫跳跃, 滑模控制, 奇异系统方法, 时变时滞系统, 随机稳定性

Abstract:

This paper studies the sliding mode controller design problem for uncertain continuous time-varying delay systems with the semi-Markov jump. Firstly, by studying the dynamic characteristics of the system, combined with the sliding mode surface, a singular system is established to describe the holonomic dynamics of the sliding mode. Then, building an appropriate Lyapunov functional by taking into account more information about time delay, a sufficient condition that guarantees the existence of sliding mode surface and the stochastic stability of sliding mode dynamics is given. Based on this, a sliding mode controller is designed to make the closed-loop system finally converge to the sliding mode surface. Finally, a numerical example is given to show the effectiveness of the developed approach.

Key words: Semi-Markov jump, Sliding mode control, Singular system approach, Time-varying delay systems, Stochastic stability

中图分类号:

O193

付亲宏, 熊良林, 张海洋, 秦娅, 权沈爱. 具有半马尔可夫跳跃的时变时滞系统的滑模控制研究[J]. 数学物理学报, 2023, 43(2): 549-562.

Fu Qinhong, Xiong Lianglin, Zhang Haiyang, Qin Ya, Quan Shenai. Sliding Mode Control for Time-Varying Delay Systems with Semi-Markov Jump[J]. Acta mathematica scientia,Series A, 2023, 43(2): 549-562.

图/表 4

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