×

Delay-dependent stability criteria for a class of networked control systems with multi-input and multi-output. (English) Zbl 1138.34035

The paper deals with the problem of delay-dependent stability for networked control systems (NCSs) with structured uncertainties and multiple state time-delays. In view of multi-input and multi-output (MIMO) NCSs with many independent sensors and actuators, a continuous time model of NCSs with distributed time-delays and uncertainties is proposed. Based on Lyapunov stability theory combined with linear matrix inequalities (LMIs) techniques, some new delay-dependent stability criteria for the system in terms of LMIs are derived. The proposed criteria give a possibility to analyze the delay-dependent asymptotic stability and obtain maximum allowable delay bound (MADB) of NCSs with uncertainties and multiple time-delays. Compared with other criteria, the proposed criteria give a much less conservative MADB and more general results. Numerical example and simulation show that the proposed criteria are effective.

MSC:

34K20 Stability theory of functional-differential equations
92C20 Neural biology
93C23 Control/observation systems governed by functional-differential equations
93D09 Robust stability
34K35 Control problems for functional-differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Halevi, Y.; Ray, A., Integrated communication and control systems: part I—analysis, ASME J dyn syst, measure control, 110, 4, 367-373, (1988)
[2] Nilsson J. Real-time control systems with delays. PhD dissertation, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, 1998.
[3] Walsh, G.C.; Ye, H.; Bushnell, L.G., Stability analysis of networked control systems, IEEE trans control syst technol, 10, 3, 438-446, (2002)
[4] Zhang, W.; Branicky, M.S.; Phillips, S.M., Stability of networked control systems, IEEE control syst mag, 21, 84-99, (2001)
[5] Lei X, Zhang JM, Wang SQ. Stability analysis of networked control systems, in: Proceedings of the first international conference on machine learning and cybernetics, vol. 1, 2002. p. 757-9.
[6] Kim, D.S.; Lee, Y.S.; Kwon, W.H.; Park, H.S., Maximum allowable delay bounds of networked control systems, Control eng practice, 11, 1301-1313, (2003)
[7] Wang CH, Wang YF, Gao HJ. Compensation time-varying in networked control systems via delay-dependent stabilization approach, in: Proceedings of the 2004 IEEE international conference on control applications, vol. 2, 2004. p. 248-53.
[8] Park, J.H., Robust stabilization for dynamic systems with multiple time varying delays and nonlinear uncertainties, J opt theory appl, 108, 155-174, (2001) · Zbl 0981.93069
[9] Lien, C.H.; Chen, J.D., Discrete-delay-independent and discrete delay dependent criteria for a class of neutral systems, J dyn syst measure, control, 125, 33-41, (2003)
[10] Moon, Y.S.; Park, P.G.; Kwon, W.H.; Lee, Y.S., Delay-dependent robust stabilization of uncertain state-delayed systems, Int J control, 74, 14, 1447-1455, (2001) · Zbl 1023.93055
[11] Cao, Y.Y.; Sun, Y.X., Delay-dependent robust stabilization of uncertain systems with multiple state delays, IEEE trans automat control, 43, 11, 1608-1612, (1998) · Zbl 0973.93043
[12] de Souza, C.E.; Li, X., Delay-dependent robust H∞ control of uncertain linear state-delayed systems, Automatica, 35, 1313-1321, (1999) · Zbl 1041.93515
[13] Su, T.J.; Lu, C.Y.; Tsai, J.S.H., LMI delay-dependent robust stability criteria for uncertain systems with multiple-state delays, IEEE trans circuits syst, 49, 2, 253-256, (2002) · Zbl 1368.93505
[14] He, Y.; Wu, M.; She, J.H.; Liu, G.P., Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Syst control lett, 51, 57-65, (2004) · Zbl 1157.93467
[15] Wu, M.; He, Y.; She, J.H.; Liu, G.P., Delay-dependent criteria for robust stability of time-varying delays systems, Automatica, 40, 3, 1435-1439, (2004) · Zbl 1059.93108
[16] Kwon, O.M.; Park, Ju H., On improved delay-dependent robust control for uncertain time-delay systems, IEEE trans automat control, 49, 11, 1991-1995, (2004) · Zbl 1365.93370
[17] Lien, C.H., Further results on delay-dependent robust stability of uncertain fuzzy systems with time-varying delay, Chaos, solitons & fractals, 28, 2, 422-427, (2006) · Zbl 1091.93022
[18] Sun, J.T., Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control, Chaos, solitons & fractals, 21, 1, 143-150, (2004) · Zbl 1048.37509
[19] Huang, X.; Cao, J.D.; Huang, D.S., LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks, Chaos, solitons and fractals, 24, 3, 885-898, (2005) · Zbl 1071.82538
[20] Zhang, Y.P.; Sun, J.T., Delay-dependent stability criteria for coupled chaotic systems via unidirectional linear error feedback approach, Chaos, solitons & fractals, 22, 1, 199-205, (2004) · Zbl 1089.93018
[21] Liu, X.W.; Zhang, H.B.; Zhang, F.L., Delay-dependent stability of uncertain fuzzy large-scale systems with time delays, Chaos, solitons & fractals, 26, 1, 147-158, (2005) · Zbl 1080.34058
[22] Li, C.D.; Liao, X.F.; Zhang, R., Delay-dependent exponential stability analysis of bi-directional associative memory neural networks with time delay: an LMI approach, Chaos, solitons & fractals, 24, 4, 1119-1134, (2005) · Zbl 1101.68771
[23] Zhang, Q.; Wei, X.P.; Xu, J., Delay-dependent exponential stability of cellular neural networks with time-varying delays, Chaos, solitons & fractals, 23, 4, 1363-1369, (2005) · Zbl 1094.34055
[24] Tu, F.H.; Liao, X.F.; Zhang, W., Delay-dependent asymptotic stability of a two-neuron system with different time delays, Chaos, solitons & fractals, 28, 2, 437-447, (2006) · Zbl 1084.68109
[25] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004
[26] Su, J.H., Further results on the robust stability of linear systems with a single time delay, Syst control lett, 23, 375-379, (1994) · Zbl 0805.93045
[27] Li, X.; de Souza, C.E., Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach, IEEE trans automat control, 42, 1144-1148, (1997) · Zbl 0889.93050
[28] Liu, P.L.; Su, T.J., Robust stability of interval time-delay systems with delay-dependence, Syst control lett, 33, 231-239, (1998) · Zbl 0902.93052
[29] Lu, C.Y.; Tsai, J.S.H.; Su, T.J., On improved delay-dependent robust stability criteria for uncertain systems with multiple-state delays, IEEE trans circuits syst, 49, 2, 253-256, (2002) · Zbl 1368.93505
[30] Liu, X.W.; Zhang, H.B., New stability criterion of uncertain systems with time-varying delay, Chaos, solitons & fractals, 26, 5, 1343-1348, (2005) · Zbl 1075.34072
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.