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State feedback stabilization of time-varying delay uncertain systems: A delay decomposition approach. (English) Zbl 1257.93076

Summary: This paper focuses on the problem of asymptotic stabilization for time-varying delay uncertain systems. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stabilization criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Based on this, a delay-dependent sufficient condition for the existence of a state feedback controller ensuring stability of the closed-loop dynamics is proposed. Then, based on the Lyapunov method, a delay-dependent stabilization criterion is devised by taking the relationship between terms in the Leibniz-Newton formula into account. Integral Inequality Approach (IIA) and delay decomposition approach are used to express this relationship and an LMIs-based algorithm to design the controller stabilizing the system.

MSC:

93D15 Stabilization of systems by feedback
93C41 Control/observation systems with incomplete information
93C15 Control/observation systems governed by ordinary differential equations
93B40 Computational methods in systems theory (MSC2010)
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[1] Boyd, S. L.; Ghaoui, E. L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), Studies in Applied Mathematics, SIAM: Studies in Applied Mathematics, SIAM Philadelphia
[2] Dey, R.; Ghosh, S.; Ray, G.; Rakshit, A., State feedback stabilization of uncertain linear time-delay systems: A nonlinear matrix inequality approach, Numer. Linear Algebra Appl., 18, 351-361 (2011) · Zbl 1249.93145
[3] Fridman, E.; Shaked, U., An improved stabilization method for linear time delay system, IEEE Trans. Automat. Control, 47, 11, 1931-1937 (2002) · Zbl 1364.93564
[4] Han, Q. L., Robust stability of uncertain delay-differential systems of neutral type, Automatica, 38, 719-723 (2002) · Zbl 1020.93016
[5] Gu, K.; Kharitonov, V.; Chen, J., Stability of Time-delay Systems (2003), Birkhauser: Birkhauser Boston · Zbl 1039.34067
[6] Han, Q. L., A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices, Internat. J. Syst. Sci., 36, 469-475 (2005) · Zbl 1093.34037
[7] He, Y.; Wu, M.; She, J. H.; Liu, G. P., Parameter dependent Lyapunov functional for stability of time delay systems with polytopic uncertainties, IEEE Trans. Automat. Control, 49, 5, 828-832 (2004) · Zbl 1365.93368
[8] 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
[9] Liu, P. L., Robust exponential stability for uncertain time-varying delay systems with delay dependence, J. Franklin Inst., 346, 10, 958-968 (2009) · Zbl 1192.34086
[10] Moon, Y. S.; Park, P.; Kwon, W. H.; Lee, Y. S., Delay-dependent robust stabilization of uncertain sate delayed system, Internat. J. Control, 74, 1447-1455 (2001) · Zbl 1023.93055
[11] S. Niculescu, A.T. Neto, J.M. Dion, D. Luc, Roust stability and stabilization of uncertain linear systems with state delay: multiple delay case (II), in: Proceedings of IFAC Symposium on Robust Control Design, Brasil, 1994, pp. 469-474.
[12] Parlakci, M. N.A., Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time delay systems, Internat. J. Robust Nonlinear Control, 16, 599-636 (2006) · Zbl 1128.93380
[13] Parlakci, M. N.A., Robust stability of uncertain time-varying state-delayed systems, IEE Proc. Control Theory Appl., 153, 469-477 (2006)
[14] Xi, L.; De Souza, C. E., Criteria for robust stability and stabilization of uncertain linear systems with state delays, Automatica, 33, 9, 1657-1662 (1999) · Zbl 1422.93151
[15] Xu, S.; Lam, J.; Zou, Y., Further results on delay-dependent robust stability conditions of uncertain neutral systems, Internat. J. Robust Nonlinear Control, 15, 233-246 (2005) · Zbl 1078.93055
[16] Wu, M.; He, Y.; She, J. H.; Liu, G. P., Delay-dependent criteria for robust stability of time-varying delay systems, Automatica, 40, 1435-1439 (2004) · Zbl 1059.93108
[17] Zhu, X. L.; Yang, G. H., Jensen integral inequality approach to stability analysis of continuous-time systems with time-varying delay, IEE Proc. Control Theory Appl., 2, 6, 524-534 (2008)
[18] Zhu, X. L.; Yang, G. H., New results of stability analysis for systems with time-varying delay, Internat. J. Robust Nonlinear Control, 20, 596-606 (2010) · Zbl 1185.93112
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