一类非线性时滞系统的采样控制

樊丽颖; 武俊峰

一类非线性时滞系统的采样控制

1.
哈尔滨理工大学应用数学系, 哈尔滨 150080
2. 哈尔滨理工大学自动化学院, 哈尔滨 150080

基金项目: 2011年黑龙江省教育厅科学技术研究项目(12511109)

详细信息

中图分类号: TP 13
计量
- 文章访问数: 1699
- HTML全文浏览量: 190
- PDF下载量: 536
- 被引次数: 0
出版历程
- 收稿日期: 2011-09-20
- 网络出版日期: 2013-01-31

Sampled-data control for a class of nonlinear time-delay systems

1.
Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
2. School of Automation, Harbin University of Science and Technology, Harbin 150080, China

摘要

摘要: 针对于采样区间具有已知上界的非线性时滞系统,分别考虑了常采样和变采样两种情况下的采样控制问题.目标是设计一个状态反馈采样控制器,使得闭环系统指数稳定,并且满足给定的性能指标.基于输入延迟方法,可以将采样控制系统转化成具有时变延迟的连续系统.引入了新的时间依赖Lyapunov函数,这些Lyapunov函数在下一个采样时间到来之前没有增长.以线性矩阵不等式(LMI, Linear Matrix Inequality)的形式给出了具有时变延迟的非线性扰动系统指数稳定的充分条件.仿真结果说明了所提方法可以提高系统的抗扰能力.
- 非线性系统 /
- 指数稳定 /
- 采样控制 /
- 输入延迟
Abstract: The problem of sampled-data control was investigated for a class of nonlinear time-delay perturbed systems, where the upper bound of sampling intervals was known and both constant sampling and variable sampling were considered. The objective is to design a state-feedback sampled-data controller, which guarantees the closed-loop system exponentially stable and satisfies given performance index. By applying an input delay approach, the sampled-data control system was transformed into a continuous time-delay system. The novel time-dependent Lyapunov functions were introduced, which did not grow before the arrival of the next sampling time. By linear matrix inequality(LMI) approach, sufficient conditions were obtained, under which the nonlinear time-delay perturbed systems were exponentially stable. And simulation results show that the proposed method can improve the immunity of system.
- nonlinear system /
- exponential stability /
- sampled-data control /
- input delay

HTML全文

参考文献(1)

[1] Basar T,Bernard P.Systems and control:foundation and applications, H_∞ optimal control and related minimax design problems.A dynamic game approach[M].Boston:Birkhanser,1995:102-108 [2] Fridman E,Seuret A,Richard J.Robust sampled-data stabilization of linear systems:an input delay approach[J].Automatica,2004,40(8):1441-1446 [3] Fridman E.A refined input delay approach to sampled-data control[J].Automatica,2010,46(2):421-427 [4] Hu Lisheng,Lam J,Cao Yongyan,et al.A linear matrix inequality(LMI) approach to robust H₂ sampled-data control for linear uncertain systems[J].IEEE Transactions on Systems,Man and Cybernetics,Part B,2003,33(1):149-155 [5] Gao Huijin,Wu Junli,Shi Peng.Robust sampled-data H_∞ control with stochastic sampling[J].Automatica,2009,45(7):1729-1736 [6] Naghshtabrizi P,Hespanha J,Teel A R.Exponential stability of impulsive systems with application to uncertain sampled-data systems[J].Systems & Control Letters,2008,57(5):378-385 [7] Liu Huiling,Peng Shiguo.Exponential stabilization of nonlinear control systems with infinite delay[J].Journal of Guangdong University of Technology,2007,24(4):22-24 [8] Jin Huiyu,Yin Baoqun.New conditions for the exponential stability of nonlinear sampled-data systems[J].Control Theory & Applications,2009,26(8):821-826 [9] Boyd S,El Ghaoui L,Feron E,et al.Linear matrix inequalities in systems and control theory [M].Philadelphia:SIAM Frontier Series,1994: 92- 98 [10] Peet M M.Exponentially stable nonlinear systems have polynomial Lyapunov functions on bounded regions[J].IEEE Transactions on Automatic Control,2009,54(5):979-987 [11] Hu Bo,Michel A N.Robustness analysis of digital feedback control systems with time-varying sampling periods[J].Journal of the Franklin Institute,2000,337(2):117-130 [12] Fridman E.A new Lyapunov technique for robust control of systems with uncertain non-small delays[J].IMA Journal of Math Contr & Information,2006,23(2):165-179 [13] Papachristodoulou A,Peet M M,Niculescu S I.Stability analysis of linear systems with time-varying delays:delay uncertainty and quenching//Proceedings of the 46^th IEEE Decision and Control.New Orleans,USA:Institute of Electrical and Electronic Engineers Inc,2007:2117-2122

施引文献

资源附件(0)

访问统计