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Passivity-based control for Markovian jump systems via retarded output feedback. (English) Zbl 1242.93040
Summary: This paper is concerned with the problem of passivity-based control for Markovian jump systems via retarded output feedback controllers. A delay-dependent passivity criterion is obtained in terms of linear matrix inequalities. Based on this, a sufficient condition is proposed for the design of a retarded output feedback controller which ensures that the closed-loop system is passive. By using the sequential linear programming matrix method, a desired retarded output feedback controller can be constructed. Numerical examples are provided to demonstrate the advantage and effectiveness of the proposed method.
93B35Sensitivity (robustness) of control systems
60J75Jump processes
93B52Feedback control
90C05Linear programming
[1]M.V. Basin, D. Calderon-Alvarez, Alternative optimal filter for linear systems with multiple state and observation delays. Int. J. Innov. Comput. Inf. Control 4, 2889–2898 (2008)
[2]E.K. Boukas, Free-weighting matrices delay-dependent stabilization for systems with time-varying delays. ICIC Express Lett. 2, 167–173 (2008)
[3]E.-K. Boukas, Z.-K. Liu, Deterministic and Stochastic Time Delay Systems (Birkhäuser, Boston, 2002)
[4]B. Du, J. Lam, Stability analysis of static recurrent neural networks using delay-partitioning and projections. Neural Netw. 22, 343–347 (2009) · doi:10.1016/j.neunet.2009.03.005
[5]Z. Fei, H. Gao, P. Shi, New results on stabilization of Markovian jump systems with mode-dependent time delay. Automatica 45, 2300–2306 (2009) · Zbl 1179.93170 · doi:10.1016/j.automatica.2009.06.020
[6]E. Fridman, New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems. Syst. Control Lett. 43, 309–319 (2001) · Zbl 0974.93028 · doi:10.1016/S0167-6911(01)00114-1
[7]Y. Fu, G. Duan, Stochastic stabilizability and passive control for time-delay systems with Markovian jumping parameters, in 8th International Conference on Control, Automation, Robotics and Vision, Kunming, China, December (2004), pp. 1757–1761
[8]C. Gong, B. Su, Delay-dependent robust stabilization for uncertain stochastic fuzzy system with time-varying delays. Int. J. Innov. Comput. Inf. Control 5, 1429–1440 (2009)
[9]K. Gu, V.L. Kharitonov, J. Chen, Stability of Time-Delay Systems (Birkhäuser, Boston, 2003)
[10]Y. He, Q.-G. Wang, L. Xie, C. Lin, Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Trans. Autom. Control 52, 293–299 (2007) · doi:10.1109/TAC.2006.887907
[11]H. Karimi, H. Gao, LMI-based H synchronization of second-order neutral master–slave systems using delayed output feedback control. Int. J. Control. Autom. Syst. 7, 371–380 (2009) · doi:10.1007/s12555-009-0306-5
[12]F. Leibfritz, An LMI-based algorithm for designing suboptimal static H 2 and H output feedback controllers. SIAM J. Control Optim. 39, 1711–1735 (2001) · Zbl 0997.93032 · doi:10.1137/S0363012999349553
[13]H. Li, B. Chen, Q. Zhou, S. Fang, Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays. Phys. Lett. A 372, 3385–3394 (2008) · Zbl 1220.82085 · doi:10.1016/j.physleta.2008.01.060
[14]H. Li, B. Chen, Q. Zhou, W. Qian, Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 39, 94–102 (2009) · doi:10.1109/TSMCB.2008.2002812
[15]R. Lozano, B. Brogliato, O. Egeland, B. Maschke, Dissipative Systems Analysis and Control: Theory and Applications (Springer, London, 2002)
[16]M.S. Mahmoud, Passivity and passification of jump time-delay systems. IMA J. Math. Control Inf. 23, 193–209 (2006) · Zbl 1095.93017 · doi:10.1093/imamci/dni053
[17]S.K. Nguang, W. Assawinchaichote, P. Shi, H filter for uncertain Markovian jump nonlinear systems: an LMI approach. Circuits Syst. Signal Process. 28, 853–874 (2007) · Zbl 1146.93381 · doi:10.1007/s00034-007-9002-y
[18]S.-I. Niculescu, R. Lozano, On the passivity of linear delay systems. IEEE Trans. Autom. Control 46, 460–464 (2001) · Zbl 1056.93610 · doi:10.1109/9.911424
[19]M. Parlakci, Robust stability of uncertain neutral systems: a novel augmented Lyapunov functional approach. IET Control Theory Appl. 1, 802–809 (2007) · doi:10.1049/iet-cta:20050517
[20]C. Peng, Y. Tian, Improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay. IET Control Theory Appl. 2, 752–761 (2008) · doi:10.1049/iet-cta:20070362
[21]K. Pyragas, Continuous control of chaos by self-controlling feedback. Phys. Lett. A 170, 421–428 (1992) · doi:10.1016/0375-9601(92)90745-8
[22]J. Qiu, K. Lu, New robust passive stability criteria for uncertain singularly Markov jump systems with time delays. ICIC Express Lett. 3, 651–656 (2009)
[23]P. Shi, M. Karan, C.Y. Kaya, Robust Kalman filter design for Markovian jump linear systems with norm-bounded unknown nonlinearities. Circuits Syst. Signal Process. 24, 135–150 (2005) · Zbl 1136.93450 · doi:10.1007/s00034-004-0702-2
[24]P. Shi, Y. Xia, G.P. Liu, D. Rees, On designing of sliding-mode control for stochastic jump systems. IEEE Trans. Autom. Control 51, 97–103 (2006) · doi:10.1109/TAC.2005.861716
[25]X. Sun, Q. Zhang, Delay-dependent robust stabilization for a class of uncertain singular delay systems. Int. J. Innov. Comput. Inf. Control 5, 1231–1242 (2009)
[26]G. Wang, Q. Zhang, V. Sreeram, Design of reduced-order H filtering for Markovian jump systems with mode-dependent time delays. Signal Process. 89, 187–196 (2009) · Zbl 1155.94337 · doi:10.1016/j.sigpro.2008.08.004
[27]L. Wu, W. Zheng, Passivity-based sliding mode control of uncertain singular time-delay systems. Automatica 45, 2120–2127 (2009) · Zbl 1175.93065 · doi:10.1016/j.automatica.2009.05.014
[28]L. Wu, W.X. Zheng, Robust passivity analysis of delayed singular systems subject to parametric uncertainties, in Proc. IEEE Int. Symp. on CAS, Taipei, Taiwan (2009), pp. 2890–2893
[29]S. Xu, Y. Chu, J. Lu, Y. Zou, Exponential dynamic output feedback controller design for stochastic neutral with distributed delays. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 36, 540–547 (2006) · doi:10.1109/TSMCA.2006.871648
[30]S. Xu, J. Lam, X. Mao, Delay-dependent H control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Trans. Circuits Syst. I 54, 2070–2077 (2007) · doi:10.1109/TCSI.2007.904640
[31]X. Yao, L. Wu, W. Zheng, C. Wang, Passivity analysis and passification of Markovian jump systems. Circuit Syst. Signal Process. 29, 709–725 (2010) · Zbl 1196.94032 · doi:10.1007/s00034-010-9166-8
[32]W. Zhang, T. Wang, S. Tong, Delay-dependent stabilization conditions and control of T-S fuzzy systems with time-delay. ICIC Express Lett. 3, 871–876 (2009)