# zbMATH — the first resource for mathematics

New robust stability condition for uncertain neutral systems with discrete and distributed delays. (English) Zbl 1198.93170
Summary: The problem of robust stability for uncertain linear neutral systems with discrete and distributed delays is considered. The uncertainties under consideration are norm bounded, and possibly time varying. Some novel delay-dependent stability criteria are derived and formulated in the form of a linear matrix inequalities (LMIs) by a new class of Lyapunov-Krasovskii functionals which is constructed based on the descriptor model of the system and the method of decomposition. The new criteria are less conservative than the existing ones. Numerical examples illustrate that the proposed criteria are effective and achieve significant improvement over the results proposed in previous paper.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### MSC:
 93D09 Robust stability 93C23 Control/observation systems governed by functional-differential equations
Full Text:
##### References:
 [1] Hale, J.K.; Verduyn Lunel, S.M., Introduction to functional differential equations, (1993), Springer-Verlag New York · Zbl 0787.34002 [2] Yang, Xiao-Song, Liapunov asymptotic stability and zhukovskij asymptotic stability, Chaos, solitons and fractals, 13, 11, 1995-1999, (2000) · Zbl 0953.34046 [3] Tian, Junkang; Zhong, Shouming; Xiong, Lianglin, Delay-dependent absolute stability of lurie control systems with multiple time-delays, Appl math comput, 188, 379-384, (2007) · Zbl 1114.93048 [4] Liu, Duyu; Zhong, Shouming; Xiong, Lianglin, On robust stability of uncertain neutral systems with multiple delays, Chaos, solitons and fractals, 39, 2332-2339, (2009) · Zbl 1197.34139 [5] Tu, Fenghua; Liao, Xiaofeng; Zhang, Wei, Delay-dependent asymptotic stability of a two-neuron system with different time delays, Chaos, solitons and fractals, 2, 28, 437-447, (2006) · Zbl 1084.68109 [6] Park, J.H.; Kwon, O.M., Chaos, LMI optimization approach to stabilization of time-delay chaotic systems, Solitons & fractals, 2, 23, 445-450, (2005) · Zbl 1061.93509 [7] Liu, Xingwen; Zhang, Hongbin, New stability criterion of uncertain systems with time-varying delay, Chaos, solitons and fractals, 5, 26, 1343-1348, (2005) · Zbl 1075.34072 [8] Xiong, Wenjun; Liang, Jinling, Novel stability criteria for neutral systems with multiple time delays, Chaos, solitons and fractals, 5, 32, 1735-1741, (2007) · Zbl 1146.34330 [9] Li, Hong; Li, Houbiao; Zhong, Shouming, Stability of neutral type descriptor system with mixed delays, Chaos, solitons and fractals, 5, 33, 1796-1800, (2007) · Zbl 1156.34347 [10] Hu, G.; Hu, G., Some simple stability criteria of neutral delay-differential systems, Appl math comput, 80, 257-271, (1996) · Zbl 0878.34063 [11] Slemrod, M.; Infante, E.F., Asymptotic stability criteria for linear systems of differential equations of neutral type and their discrete analogues, J math anal appl, 38, 399-415, (1972) · Zbl 0202.10301 [12] Xiong, Lianglin; Zhong, Shouming; Tian, Junkang, Novel robust stability criteria of uncertain neutral systems with discrete and distributed delays, Chaos, solitons and fractals, 40, 771-777, (2009) · Zbl 1197.93132 [13] Yan Huaicheng, Huang Xinhan, Wang Min, Zhang Hao. New delay-dependent stability criteria of uncertain linear systems with multiple time-varying state delays. Chaos, Solitons and Fractals 2008;37(1):157-65. · Zbl 1156.34059 [14] Kolmanovskii, V.B.; Richard, J.-P., Stability of some linear systems with delays, IEEE trans automatic control, 44, 984-989, (1999) · Zbl 0964.34065 [15] Niculescu S-I. Further remarks on delay-dependent stability of linear neutral systems. In: Proceedings of MTNS 2000, Perpigan, France. [16] Han, Qinglong, Robust stability of uncertain delay-differential systems of neutral type, Automatica, 38, 719-723, (2002) · Zbl 1020.93016 [17] Lien, C.-H.; Yu, K.W.; Hsieh, J.G., Stability conditions for a class of neutral systems with multiple time delays, J math anal appl, 245, 20-27, (2000) · Zbl 0973.34066 [18] Gu, K.; Niculescu, S.-I., Further remarks on additional dynamics in various model transformations of linear delay systems, IEEE trans automatic control, 46, 497-500, (2001) · Zbl 1056.93511 [19] Han, Qinglong, A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays, Automatica, 40, 1791-1796, (2004) · Zbl 1075.93032 [20] Xie, L., Output feedback $$H \infty$$ control of systems with parameter uncertainty, Int J control, 63, 741-750, (1996) · Zbl 0841.93014 [21] Gu, K., An integral inequality in the stability problem of time delay systems, () [22] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004 [23] Chen, J.D.; Lien, C.H.; Fan, K.K.; Chou, J.H., Criteria for asymptotic stability of a class of neutral systems via a LMI approach, IEE proc control theory appl, 148, 6, 442-447, (2001) [24] Yue, D.; Won, S.; Kwon, O., Delay dependent stability of neutral systems with time delay: an LMI approach, IEE proc control theory appl, 150, 23-27, (2003) [25] Chen, Wuhua; Zheng, Weixing, Delay-dependent robust stabilization for uncertain neutral systems with distributed delays, Automatica, 43, 1, 95-104, (2007) · Zbl 1140.93466 [26] Fridman, E., New lyapunov – krasovskii functionals for stability of linear retarded and neutral type systems, Syst control lett, 43, 309-319, (2001) · Zbl 0974.93028 [27] Fridman, E.; Shaked, U., A descriptor system approach to $$H \infty$$ control of linear time-delay systems, IEEE trans automatic control, 47, 253-270, (2002) · Zbl 1364.93209
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.