zbMATH — the first resource for mathematics

Robust output feedback \(H_{}\) control of uncertain Markovian jump systems with mode-dependent time-delays. (English) Zbl 1194.93181
Summary: This paper describes the synthesis of robust output feedback \(H_{\infty }\) control for a class of uncertain Markovian jump linear systems with time-delays which are time-varying and depend on the system modes of operation. Under the assumption of known bounds of system uncertainties and the control system gain variations, we present sufficient conditions on the existence of robust stochastic stability and \(\gamma \)-disturbance \(H_{\infty }\) attenuation. Through the changes of variables and Schur complements, these sufficient conditions can be rewritten in a set of coupled linear matrix inequalities, with which, robust control can be easily constructed. As an added advantage, the control design depends only on \(p^o_{mj,t}\), the measured parameter of Markovian jumping at time \(t\), which might be corrupted by measurement noises. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.

93D15 Stabilization of systems by feedback
15A39 Linear inequalities of matrices
93B35 Sensitivity (robustness)
93B36 \(H^\infty\)-control
93E03 Stochastic systems in control theory (general)
Full Text: DOI
[1] Benjelloun, K and Boukas, EK. 1997. ”Independent delay sufficient conditions for robust stability of uncertain linear time-delay systems with jumps”. Proc. Amer. Contr. Conf. 1997, Albuquerque, New Mexico. pp.3814–3815.
[2] Benjelloun K, IEEE Trans. Automat. Contr. 43 pp 1456– (1998)
[3] Benjelloun, K, Boukas, EK and Costa, OLV. 1999. ”Hcontrol for linear time-delayed systems with Markovian jumping parameters”. Proc. IEEE Conference on Decision and Control (CDC’99). 1999, Phoenix, Arizona. pp.1567–1572.
[4] Boukas, EK and Liu, ZK. 2000. ”Output feedback guaranteed cost control for uncertain time-delay systems with Markov jumps”. Proc. Amer. Contr. Conf. 2000, Chicago, Illinois. pp.2784–2788.
[5] Boukas, EK and Liu, ZK. 2001. ”Output feedback robust stabilization of jump linear system with mode-dependent time-delays”. Proc. Amer. Contr. Conf. 2001, Arlington, VA. pp.4683–4688.
[6] Boukas EK, Deterministic and Stochastic Time Delay Systems (2002)
[7] DOI: 10.1109/TAC.1985.1103907 · Zbl 0571.93035
[8] DOI: 10.1137/S0363012992238679 · Zbl 0843.93076
[9] DOI: 10.1109/9.827358 · Zbl 0983.93075
[10] DOI: 10.1109/CDC.1989.70216
[11] DOI: 10.1109/TAC.2003.820165 · Zbl 1364.93369
[12] DOI: 10.1016/j.sysconle.2004.02.012 · Zbl 1157.93438
[13] DOI: 10.1049/ip-cta:20040844
[14] DOI: 10.1002/(SICI)1099-1239(200003)10:3<157::AID-RNC484>3.0.CO;2-K · Zbl 0951.93032
[15] Famularo, D, Abdallah, CT, Jadbabaie, A, Dorato, P and Haddad, WM. 1998. ”Robust non-fragile LQ controller: the static feedback case”. Proc. Amer. Contr. Conf (ACC’98). 1998, Philadelphia, Pennsylvania. pp.1109–1113.
[16] DOI: 10.1109/TAC.2002.804462 · Zbl 1364.93564
[17] DOI: 10.1080/0020717021000049151 · Zbl 1023.93032
[18] DOI: 10.1016/0005-1098(96)00033-7 · Zbl 0855.93025
[19] Ge SS, IEEE Trans. Syst. Man, Cybern. B 38 pp 671– (2002)
[20] DOI: 10.1016/j.automatica.2005.01.011 · Zbl 1078.93046
[21] Hale J, Theory of Functional Differential Equations, 2. ed. (1977) · Zbl 0352.34001
[22] DOI: 10.1109/9.618239 · Zbl 0900.93075
[23] Kim, JH, Lee, SK and Park, HB. 1999. ”Robust and non-fragileHcontrol of parameter uncertain time-varying delay systems”. 38th Annual Conference Proceedings of the SICE Annual. 1999, Morioka. pp.927–932.
[24] DOI: 10.1109/TAC.1972.1099894 · Zbl 0262.15015
[25] Kushner HJ, Stochastic Stability and Control (1967)
[26] Mariton M, Jump Linear Systems in Automatic Control (1990)
[27] DOI: 10.1109/9.67303 · Zbl 0764.93084
[28] DOI: 10.1002/(SICI)1099-1239(19980715)8:8<669::AID-RNC337>3.0.CO;2-W · Zbl 0921.93012
[29] DOI: 10.1080/00207170110067116 · Zbl 1023.93055
[30] Nassiri-Toussi, K and Caines, PE. 1991. ”On the adaptive stabilization and ergodic behaviour of stochastic jump parameter systems via nonlinear filtering”. Proc. IEEE Conference on Decision and Control (CDC’91). 1991, Brighton, England. pp.1784–1785. · Zbl 0793.93106
[31] DOI: 10.1109/9.754838 · Zbl 0957.34069
[32] DOI: 10.1109/TAC.2005.851456 · Zbl 1365.93245
[33] DOI: 10.1109/9.995042 · Zbl 1364.93672
[34] DOI: 10.1109/TSP.2003.815373 · Zbl 1369.94314
[35] DOI: 10.1016/j.automatica.2004.03.004 · Zbl 1059.93108
[36] DOI: 10.1080/00207179608921866 · Zbl 0841.93014
[37] DOI: 10.1016/S0005-1098(04)00197-9
[38] DOI: 10.1109/TAC.2003.820138 · Zbl 1364.93229
[39] Yang G, Automatica 37 pp 727– (2001) · Zbl 0990.93031
[40] DOI: 10.1016/j.automatica.2003.10.012 · Zbl 1040.93069
[41] DOI: 10.1016/S0167-6911(03)00154-3 · Zbl 1157.60330
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.