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J4  2012, Vol. 46 Issue (5): 848-852    DOI: 10.3785/j.issn.1008-973X.2012.05.012
自动化技术、电气工程     
具有区间时变时滞的中立型系统稳定性分析
毛维杰,张媛媛
浙江大学 控制科学与工程学系, 浙江 杭州 310027
Stability analysis for neutral systems with interval time-varying delays
MAO Wei-jie, ZHANG Yuan-yuan
Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China
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摘要:

针对一类具有区间时变时滞的线性中立型系统,基于Lyapunov-Krasovskii泛函与改进的自由权矩阵方法,提出时滞区间依赖型稳定性条件.当时滞的变化率已知时,得到同时依赖于时滞区间和时滞变化率的稳定性条件;当时滞的变化率未知时,得到依赖于时滞区间、独立于时滞变化率的稳定性条件.所给条件进一步推广到具有范数有界不确定性的中立型系统,提出鲁棒稳定性条件.所有结果均以线性矩阵不等式的形式给出,利用线性矩阵不等式(LMI)工具求解非常方便.数值实例验证了结果的有效性.

Abstract:

Based on the Lyapunov-Krasovskii functional method and the free weighting matrix method, a delay-range-dependent stability condition is proposed for a class of linear neutral systems with interval time-varying delays. When the derivative of the delay is known, a range-dependent and rate-dependent stability condition is obtained; when the derivative of the delay is unknown, a range-dependent and rate-independent stability condition is obtained. The proposed stability condition is further extended to the neutral systems with norm-bounded uncertainties and a robust delay-range-dependent stability condition is established. As all the conditions are derived in terms of LMIs, it is very convenient to solve them by using the LMI toolbox. Finally, numerical examples are given to show the effectiveness of the proposed conditions.

出版日期: 2012-05-01
:  TP 13  
基金资助:

国家自然科学基金资助项目(61074045).

作者简介: 毛维杰(1969-),男,教授,博导,从事时滞系统控制理论与应用研究. E-mail: wjmao@iipc.zju.edu.cn
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引用本文:

毛维杰,张媛媛. 具有区间时变时滞的中立型系统稳定性分析[J]. J4, 2012, 46(5): 848-852.

MAO Wei-jie, ZHANG Yuan-yuan. Stability analysis for neutral systems with interval time-varying delays. J4, 2012, 46(5): 848-852.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2012.05.012        http://www.zjujournals.com/eng/CN/Y2012/V46/I5/848

[1] RICHARD J P. Timedelay systems: An overview of some recent advances and open problems [J]. Automatica, 2003, 39(10): 1667-1694.
[2] FRIDMAN E. New LyapunovKrasovskii functionals for stability of linear retarded and neutral type systems [J]. Systems & Control Letters, 2001, 43(4): 309-319.
[3] YUE D, WON S, KWON O. Delay dependent stability of neutral systems with time delay: an LMI approach [J]. IEE ProcControl Theory and Applications, 2003, 150(1): 23-27.
[4] HE Y, WU M, SHE J H, et al. Delaydependent robust stability criteria for uncertain neutral systems with mixed delays [J]. Systems & Control Letters, 2004, 51(1): 57-65.
[5] LI X G, ZHU X J. Stability analysis of neutral systems with mixed delays [J]. Automatica, 2008, 44(11): 2968-2972.
[6] QIAN W, LIU J, SUN Y, et al. A less conservative robust stability criteria for uncertain neutral systems with mixed delays [J]. Mathematics and Computers in Simulation, 2010, 80(5): 1007-1017.
[7] ENGELBORGHS K, LUZYANINA T, SAMAEY G. Report TW330, DDEBIFTOOL: A matlab package for bifurcation analysis for delay differential equations [R]. Belgium, Leuven: K U Leuven, 2001.
[8] MAO W J, CHU J. Dstability for linear continuoustime systems with multiple time delays [J]. Automatica, 2006, 42(9): 1589-1592.
[9] HE Y, WANG Q G, LIN C, et al. Delayrange dependent stability for systems with timevarying delay [J]. Automatica, 2007, 43(2): 371-376.
[10] JIANG X F, HAN Q L. New stability criteria for linear systems with interval timevarying delay [J]. Automatica, 2008, 44(10): 2680-2685.
[11] PENG C, TIAN Y C. Delaydependent robust stability criteria for uncertain systems with interval timevarying delay [J]. J of Computational and Applied Mathematics, 2008, 214(2): 480-494.
[12] SHAO H. New delaydependent stability criteria for systems with interval delay [J]. Automatica, 2009, 45(3): 744-749.
[13] SUN J, LIU G P, CHEN J, et al. Improved delay rangedependent stability criteria for linear systems with timevarying delays [J]. Automatica, 2010, 46(2): 466-470.
[14] YU K W, LIEN C H. Stability criteria for uncertain neutral systems with interval timevarying delays [J]. Chaos, Solitons & Fractals, 2008, 38(3): 650-657.
[15] KWON O M, PARK J H, LEE S M. On delaydependent robust stability of uncertain neutral systems with interval timevarying delays [J]. Applied Mathematics and Computation, 2008, 203(2): 843-853.
[16] KWON O M, PARK J H, LEE S M. Corrigendum to published papers in applied mathematics and computation [J]. Applied Mathematics and Computation, 2009, 215(1): 427-430.
[17] PARK J H. Global stability for neural networks of neutraltype with interval timevarying delays [J]. Chaos, Solitons & Fractals, 2009, 41(3): 1174-1181.
[18] PETERSEN I R. A stabilization algorithm for a class of uncertain linear systems [J]. Systems & Control Letters, 1987, 8(4): 351-357.

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