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Li, Tai-Fang; Zhao, Jun; Dimirovski, Georgi M.

Stability and \(L_{2}\)-gain analysis for switched neutral systems with mixed time-varying delays. (English) Zbl 1239.93103

J. Franklin Inst. 348, No. 9, 2237-2256 (2011).
Summary: This paper considers the stability and \(L_{2}\)-gain for a class of switched neutral systems with time-varying discrete and neutral delays. Some new delay-dependent sufficient conditions for exponential stability and weighted \(L_{2}\)-gain are developed for a class of switching signals with average dwell time. These conditions are formulated in terms of Linear Matrix Inequalities (LMIs) and are derived by employing free weighting matrices method. As a special case of such switching signals, we can obtain exponential stability and normal \(L_{2}\)-gain under arbitrary switching signals. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.

Cited in 25 Documents

MSC:

93D20 Asymptotic stability in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
34K40 Neutral functional-differential equations

Keywords:

exponential stability; switched neutral systems; average dwell time; linear matrix inequalities (LMIs)
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References:

[1] Liberzon, D., Switching in systems and control (2003), Birkhauser: Birkhauser Boston · Zbl 1036.93001
[2] Lin, H.; Antsaklis, P. J., Stability and stabilization of switched linear systems: a survey of recent results, IEEE Transactions on Automatic Control, 54, 2, 308-322 (2009) · Zbl 1367.93440
[3] Sun, Z. D., Sampling and control of switched linear systems, Journal of the Franklin Institute, 341, 7, 657-674 (2004) · Zbl 1064.94566
[4] Zhai, G. S.; Hu, B.; Yasuda, K.; Michel, A. N., Disturbance attenuation properties of time-controlled switched systems, Journal of the Franklin Institute, 338, 7, 765-779 (2001) · Zbl 1022.93017
[5] Wang, Z.; Lauria, S.; Fang, J.; Liu, X., Exponential stability of uncertain stochastic neural networks with mixed time-delays, Chaos, Solitons & Fractals, 32, 1, 62-72 (2007) · Zbl 1152.34058
[6] Liu, X.; Zhang, H., New stability criterion of uncertain systems with time-varying delay, Chaos, Solitons & Fractals, 26, 5, 1343-1348 (2005) · Zbl 1075.34072
[7] Zhang, L. X.; Wang, C. H.; Chen, L. J., Stability and stabilization of a class of multi-mode linear discrete-time systems with polytopic uncertainties, IEEE Transactions on Industrial Electronics, 56, 9, 3684-3692 (2009)
[8] Richard, J. P., Time-delay systems: an overview of some recent advances and open problems, Automatica, 39, 10, 1667-1694 (2003) · Zbl 1145.93302
[9] Chen, W. H.; Zheng, W. X., Delay-dependent robust stabilization for uncertain neutral systems with distributed delays, Automatica, 43, 1, 95-104 (2007) · Zbl 1140.93466
[10] Bellen, A.; Guglielmi, N.; Ruehli, A. E., Methods for linear systems of circuit delay differential equations of neutral type, IEEE Transactions on Circuits and Systems—I: Fundamental and Applications, 46, 1, 212-216 (1999) · Zbl 0952.94015
[11] Qiu, F.; Cui, B. T.; Ji, Y., Further results on robust stability of neutral system with mixed time-varying delays and nonlinear perturbations, Nonlinear Analysis: Real World Applications, 11, 2, 895-906 (2010) · Zbl 1187.37124
[12] Chen, Y.; Xue, A.; Lu, R.; Zhou, S. S., On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations, Nonlinear analysis: Theory, Methods & Applications, 68, 8, 2464-2470 (2008) · Zbl 1147.34352
[13] Zhang, K. Y.; Cao, D. Q., Further results on asymptotic stability of linear neutral systems with multiple delays, Journal of the Franklin Institute, 344, 6, 858-866 (2007) · Zbl 1117.93365
[14] Li, M.; Liu., L., A delay-dependent stability criterion for linear neutral delay systems, Journal of the Franklin Institute, 346, 1, 33-37 (2009) · Zbl 1298.34153
[15] Yin, C.; Zhong, S. M.; Chen, W. F., On delay-dependent robust stability of a class of uncertain mixed neutral and Lur’e dynamical systems with interval time-varying delays, Journal of the Franklin Institute, 347, 9, 1623-1642 (2010) · Zbl 1202.93105
[16] Kim, D. K.; Park, P. G.; Ko., J. W., Output-feedback \(H_∞\) control of systems over communication networks using a deterministic switching system approach, Automatica, 40, 7, 1205-1212 (2004) · Zbl 1056.93527
[17] Sun, X. M.; Zhao, J.; Hill, D. J., Stability and \(L_2\)-gain analysis for switched delay system: a delay-dependent method, Automatica, 42, 10, 1769-1774 (2006) · Zbl 1114.93086
[18] Sun, X. M.; Wang, W.; Liu, G. P.; Zhao, J., Stability analysis for linear switched systems with time-varying delay, IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 38, 2, 528-533 (2008)
[19] Hien, L. V.; Ha, Q. P.; Phat, V. N., Stability and stabilization of switched linear dynamic systems with time delay and uncertainties, Applied Mathematics and Computation, 210, 1, 223-231 (2009) · Zbl 1159.93351
[20] Niamsup, P., Stability of time-varying switched systems with time-varying delay, Nonlinear Analysis: Hybrid Systems, 3, 4, 631-639 (2009) · Zbl 1190.34094
[21] Phat, V. N., Switched controller design for stabilization of nonlinear hybrid systems with time-varying delays in state and control, Journal of the Franklin Institute, 347, 1, 195-207 (2010) · Zbl 1298.93290
[22] Zhang, L. X.; Shi, P., Stability, \(L_2\)-gain and asynchronous \(H_∞\) control of discrete-time switched systems with average dwell time, IEEE Transactions on Automatic Control, 54, 9, 2193-2200 (2009)
[23] Liu DY, Zhong SM, Huang YQ. Stability and \(L_2\); Liu DY, Zhong SM, Huang YQ. Stability and \(L_2\)
[24] Zhang, Y. P.; Liu, X. Z.; Zhu, H.; Zhong, S. M., Stability analysis and control synthesis for a class of switched neutral systems, Applied Mathematics and Computation, 190, 2, 1258-1266 (2007) · Zbl 1117.93062
[25] Liu, D. Y.; Zhong, S. M.; Liu, X. Z.; Huang, Y. Q., Stability analysis for uncertain switched neutral systems with discrete time-varying delay: a delay-dependent method, Mathematics and Computers in Simulation, 80, 2, 436-448 (2009) · Zbl 1185.34105
[26] Xiong, L. L.; Zhong, S. M.; Ye, M.; Wu, S. L., New stability and stabilization for switched neutral control systems, Chaos, Solitons and Fractals, 42, 3, 1800-1811 (2009) · Zbl 1198.93187
[27] Liu, D. Y.; Zhong, S. M.; Liu, X. Z.; Huang, Y. Q., Delay-dependent robust stability and control synthesis for uncertain switched neutral systems with mixed delays, Applied Mathematics and Computation, 202, 2, 828-839 (2008) · Zbl 1143.93020
[28] Sun, X. M.; Fu, J.; Sun, H. F.; Zhao, J., Stability of linear switched neutral delay systems, Proceedings of the Chinese Society of Electrical Engineering, 25, 23, 42-46 (2005)
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