﻿ 一类不确定广义时滞系统的<i>H</i><sub>∞</sub>自适应控制
 控制与决策  2019, Vol. 34 Issue (10): 2164-2170 0

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[复制中文]
XIAO Hui-min, MENG Xin. Adaptive H control for a class of uncertain singular time-delay systems[J]. Control and Decision, 2019, 34(10): 2164-2170. DOI: 10.13195/j.kzyjc.2018.0141.
[复制英文]

### 文章历史

1. 河南财经政法大学 计算机与信息工程学院, 郑州 450003;
2. 中国海洋大学 数学科学学院, 山东 青岛 266100

Adaptive H control for a class of uncertain singular time-delay systems
XIAO Hui-min 1, MENG Xin 2
1. School of Computer and Information Engineering, Henan University of Finance and Economics, Zhengzhou 450003, China;
2. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
Abstract: An integral sliding surface with a compensator is constructed for a class of uncertain singular time-delay systems with external disturbance in this paper. Firstly, based on the Lyapunov stability theory and linear matrix inequality, a robust asymptotically stability criterion is presented for sliding mode dynamics with all admissible uncertainties under some decay rate. Then, a new adaptive sliding mode control law is designed to make sure that the trajectories of the sliding mode dynamics can be driven to a region near equilibrium point in finite time. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.
0 引言

1 问题描述

 (1)

 (2)

1) 正则的和无脉冲的, 若矩阵对(E, A)是正则的和无脉冲的;

2) 稳定的, 若对于任意的ε > 0, 存在标量δ(ε) > 0, 使得对于任意初始条件φ(s)满足δ(ε), 则系统(2)的解x(t)满足x(t)→0, t→+∞;

3) 可容许的, 若系统是正则的、无脉冲的和稳定的.

2 主要结果 2.1 观测器设计

 (3)

 (4)

2.2 滑模面设计

 (5)

 (6)

 (7)

 (8)

 (9)
 (10)

 (11)

2.3 滑动模态方程可容许性分析

1) 在扰动输入w(t) = 0时, 证明滑动模态方程是可容许的;

2) 对于给定的常数γ > 0, 在零初始条件下, H性能指标(11)对于任意非零扰动w(t)恒成立.

 (12)

SRn×(n-r)为满足ETS = 0的任意列满秩向量.则滑动模态方程(9)和(10)在H性能指标下是可容许的.此时, 反馈矩阵KL可分别从式K = B+Z-TBXL = Z-TY中得到.

 (13)

 (14)

 (15)

 (16)

 (17)
 (18)
 (19)
 (20)

 (21)

 (22)

 (23)

 (24)

 (25)

2.4 滑模可达性分析

 (26)

 (27)

 (28)

 (29)

 (30)

3 仿真算例

 图 1 子系统(1)的状态响应曲线
 图 2 子系统(2)的状态响应曲线
 图 3 滑模面泛函与自适应控制器响应曲线
 图 4 自适应率响应曲线
4 结论

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