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Observer-based finite-time control of time-delayed jump systems. (English) Zbl 1207.93113
Summary: This paper provides the observer-based finite-time control problem of time-delayed Markov Jump Systems (MJS) that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The observer-based finite-time $H_\infty$ controller via state feedback is proposed to guarantee the stochastic finite-time boundedness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible disturbances and unknown time-delays. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic robust control performance of time-delay jump systems are derived. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The presented results are extended to time-varying delayed MJSs. Simulation results illustrate the effectiveness of the developed approaches.

93E15Stochastic stability
93B35Sensitivity (robustness) of control systems
60J75Jump processes
Full Text: DOI
[1] Amato, F.; Ariola, M.: Finite-time control of discrete-time linear systems, IEEE trans. Automat. control 50, 724-729 (2005)
[2] Amoto, F.; Ariola, M.; Cosentino, C.: Finite-time stabilization via dynamic output feedback, Automatica 42, 337-342 (2006) · Zbl 1099.93042 · doi:10.1016/j.automatica.2005.09.007
[3] Amoto, F.; Ambrosino, R.; Ariola, M.; Cosentino, C.: Finite-time stability of linear time-varying systems with jumps, Automatica 45, 1354-1358 (2009) · Zbl 1162.93375 · doi:10.1016/j.automatica.2008.12.016
[4] Atlans, M.: Command and control theory: a challenge to control science, IEEE trans. Automat. control 32, 286-293 (1987)
[5] Arrifano, N. S. D.; Olivera, V. A.: Robust H$\infty $ fuzzy control approach for a class of Markovian jump nonlinear systems, IEEE trans. Fuzzy syst. 14, 738-754 (2006)
[6] S.P. Boyd, L. El Ghaoui, E. Feron, Linear matrix inequalities in system and control theory, in: Society for Industrial and Applied Mathematics, Academic Press, Philadelphia, 1994. · Zbl 0816.93004
[7] Costa, O. L. V.; Filho, E. O. Assumpc√£o; Boukas, E. K.; Marques, R. P.: Constrained quadratic state feedback control of discrete-time Markovian jump linear systems, Automatica 35, 617-626 (1999) · Zbl 0933.93079 · doi:10.1016/S0005-1098(98)00202-7
[8] P. Dorato, Short time stability in linear time-varying systems, in: IRE International Convention Record, Part 4. New York, USA, 1961, pp. 83 -- 87.
[9] Doucet, A.; Johansen, A. M.; Tadic, V. B.: On solving integral equations using Markov chain Monte Carlo methods, Appl. math. Comput. 216, 2869-2880 (2010) · Zbl 1193.65217 · doi:10.1016/j.amc.2010.03.138
[10] Ei-Gohary, A.: Optimal control of an angular motion of a rigid body during infinite and finite-time intervals, Appl. math. Comput. 141, 541-551 (2003) · Zbl 1041.70022
[11] Ei-Gohary, A.; Ai-Ruzaiza, A. S.: Optimal control of non-homogenous prey -- predator models during infinite and finite-time intervals, Appl. math. Comput. 146, 495-508 (2003) · Zbl 1026.92044
[12] Feng, X.; Loparo, K. A.; Ji, Y.: Stochastic stability properties of jump linear systems, IEEE trans. Automat. control 37, 38-53 (1992) · Zbl 0747.93079
[13] He, S.; Liu, F.: Unbiased H$\infty $ filtering for neutral Markov jump systems, Appl. math. Comput. 206, 175-185 (2008) · Zbl 1152.93052 · doi:10.1016/j.amc.2008.08.046
[14] He, S.; Liu, F.: Fuzzy model-based fault detection for Markov jump systems, Int. J. Robust nonlinear control 19, 1248-1266 (2009) · Zbl 1166.93343 · doi:10.1002/rnc.1380
[15] He, S.; Liu, F.: Robust peak-to-peak filtering for Markov jump systems, Signal process. 90, 513-522 (2010) · Zbl 1177.93080 · doi:10.1016/j.sigpro.2009.07.018
[16] He, S.; Liu, F.: Stochastic finite-time stabilization for uncertain jump systems via state feedback, J. dynam. Syst., measurement control 132, 0345041-0345044 (2010)
[17] Hsiao, C.: Numerical solutions of linear time-varying descriptor systems via hybrid functions, Appl. math. Comput. 216, 1363-1374 (2010) · Zbl 1189.65131 · doi:10.1016/j.amc.2010.03.004
[18] Krasovskii, N. M.; Lidskii, E. A.: Analytical design of controllers in systems with random attributes, Automat. remote control 22, 1021-1025 (1961) · Zbl 0104.36704
[19] Kwon, O. M.; Park, J. H.: Exponential stability analysis for uncertain neural networks with interval time-varying delays, Appl. math. Comput. 212, 530-541 (2009) · Zbl 1179.34080 · doi:10.1016/j.amc.2009.02.043
[20] Moulay, E.; Dambrine, M.; Yeganefar, N.; Perruquetti, W.: Finite-time stability and stabilization of time-delay systems, Syst. control lett. 57, 561-566 (2008) · Zbl 1140.93447 · doi:10.1016/j.sysconle.2007.12.002
[21] Mao, X.: Stability of stochastic differential equations with Markovian switching, Stoch. process. Appl. 79, 45-67 (1999) · Zbl 0962.60043 · doi:10.1016/S0304-4149(98)00070-2
[22] Ning, H.; Cai, K.: Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control, IEEE trans. Syst. man cybernet. B 36, 509-519 (2006)
[23] M.A. Rami, E.L. Ghaoui, Robust stabilization of jump linear systems using linear matrix inequalities, in: IFAC Symposium on Robust Control Design, Rio de Janeiro, Brazil, 1994, pp. 148 -- 151.
[24] Sworder, D. D.; Rogers, R. O.: An LQG solution to a control problem with solar thermal receiver, IEEE trans. Automat. control 28, 971-978 (1983)
[25] Shi, P.; Boukas, E. K.: Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters, IEEE trans. Automat. control 44, 1592-1597 (1999) · Zbl 0986.93066 · doi:10.1109/9.780431
[26] Weiss, L.; Infante, E. F.: Finite time stability under perturbing forces and on product spaces, IEEE trans. Automat. control 2, 54-59 (1967) · Zbl 0168.33903
[27] Yang, Y.; Li, J.; Chen, G.: Finite-time stability and stabilization of nonlinear stochastic hybrid systems, J. math. Anal. appl. 356, 338-345 (2009) · Zbl 1163.93033 · doi:10.1016/j.jmaa.2009.02.046
[28] Zhang, X.; Chen, G.: The computation of Drazin inverse and its applications in Markov chains, Appl. math. Comput. 183, 292-300 (2006) · Zbl 1112.65038 · doi:10.1016/j.amc.2006.05.076