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Robust finite-time stabilization of uncertain singular Markovian jump systems. (English) Zbl 1252.93130
Summary: This paper focuses on the problem of robust finite-time stabilization for one family of uncertain singular Markovian jump systems. Firstly, the definitions of singular stochastic finite-time boundedness and singular stochastic H finite-time boundedness are presented. Secondly, sufficient conditions on singular stochastic finite-time boundedness are obtained for the class of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic H finite-time boundedness for the family of singular stochastic systems. Sufficient criteria are provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic finite-time boundedness and singular stochastic H finite-time boundedness, which can be reduced to a feasibility problem in the form of linear matrix inequalities with a fixed parameter, respectively. Finally, numerical examples are given to illustrate the validity of the proposed methodology.
MSC:
93E15Stochastic stability
93B36H -control
60H10Stochastic ordinary differential equations
60J27Continuous-time Markov processes on discrete state spaces
93D15Stabilization of systems by feedback
References:
[1]Kushner, H. J.: Finite-time stochastic stability and the analysis of tracking systems, IEEE trans. Automat. control 11, 219-227 (1966)
[2]Weiss, L.; Infante, E. F.: Finite time stability under perturbing forces and on product spaces, IEEE trans. Automat. control 12, 54-59 (1967)
[3]Amato, F.; Ariola, M.; Dorato, P.: Finite-time control of linear systems subject to parametric uncertainties and disturbances, Automatica 37, 1459-1463 (2001) · Zbl 0983.93060 · doi:10.1016/S0005-1098(01)00087-5
[4]Zhang, W.; An, X.: Finite-time control of linear stochastic systems, Int. J. Innovative comput. Inform. control 4, No. 3, 689-696 (2008)
[5]He, S.; Liu, F.: Robust finite-time stabilization of uncertain fuzzy jump systems, Int J. Innovative comput. Inform. control 6, No. 9, 3853-3862 (2010)
[6]Amato, F.; Ariola, M.; Dorato, P.: Finite-time stabilzation via dynamic output feedback, Automatica 42, 337-342 (2006) · Zbl 1099.93042 · doi:10.1016/j.automatica.2005.09.007
[7]Xin, D.; Liu, Y.: Finite-time stability analysis and control design of nonlinear systems, J. shandong univ. 37, 24-30 (2007)
[8]Y. Zhang, C. Liu, X. Mu, Finite-time control of delayed systems subject to exogenous disturbance, in: 2009 International Workshop on Intelligent Systems and Applications, ISA 2009, 2009, pp. 2147 – 2149.
[9]Garcia, G.; Tarbouriech, S.; Bernussou, J.: Finite-time stabilization of linear time-varying continuous systems, IEEE trans. Automat. control 54, 364-369 (2009)
[10]Ambrosino, R.; Calabrese, F.; Cosentino, C.; De, T. G.: Sufficient conditions for finite-time stability of impulsive dynamical systems, IEEE trans. Automat. control 54, 861-865 (2009)
[11]Amato, 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
[12]Li, S.; Wang, Z.; Fei, S.: Finite-time control of a bioreactor system using terminal sliding mode, Int. J. Innovative comput. Inform. control 5, No. 10B, 3495-3504 (2009)
[13]Amato, F.; Ariola, M.; Cosentino, C.: Finite-time control of discrete-time linear systems: analysis and design conditions, Automatica 46, 919-924 (2010) · Zbl 1191.93099 · doi:10.1016/j.automatica.2010.02.008
[14]Meng, Q.; Shen, Y.: Finite-time H control for linear continuous system with norm-bounded disturbance, Commun. nonlinear sci. Numer. simulat. 14, 1043-1049 (2009) · Zbl 1221.93066 · doi:10.1016/j.cnsns.2008.03.010
[15]He, S.; Liu, F.: Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities, Appl. math. Modell. 35, 2631-2638 (2011) · Zbl 1219.93143 · doi:10.1016/j.apm.2010.11.050
[16]Lewis, F. L.; Systems, A. Survey Of Linear Singular: Circuits, Syst. signal process. 22, 3-36 (1986) · Zbl 0613.93029 · doi:10.1007/BF01600184
[17]Dai, L.: Lectures notes in control and information sciences, Singular control systems 118 (1989)
[18]Ishihara, J. Y.; Terra, M. H.: On the Lyapunov theorem for singular systems, IEEE trans. Automat. control 47, 1926-1930 (2002)
[19]Mahmoud, M.; Al-Sunni, F.; Shi, Y.: Dissipativity results for linear singular time-delay systems, Int. J. Innovative comput. Inform. control 4, No. 11, 2833-2846 (2008)
[20]Wu, Z.; Park, J. H.; Su, H.; Chu, J.: Dissipativity analysis for singular systems with time-varying delays, Appl. math. Comput. 218, No. 8, 4605-4613 (2011)
[21]Masubuchi, I.; Kamime, Y.; Ohara, A.; Suda, N.: H control for descriptor systems: a matrix inequalities approach, Automatica 3, No. 4, 669-673 (1997) · Zbl 0881.93024 · doi:10.1016/S0005-1098(96)00193-8
[22]Xia, Y.; Shi, P.; Liu, G.; Rees, D.: Robust mixed H/H2 state-feedback control for continuous-time descriptor systems with parameter uncertainties, Syst. signal process. 24, No. 4, 431-443 (2005) · Zbl 1136.93338 · doi:10.1007/s00034-004-0917-2
[23]Zhang, L.; Huang, B.; Lam, J.: LMI synthesis of H2 and mixed H2/H controllers for singular systems, IEEE trans. Circuits syst. 50, No. 9, 615-626 (2003)
[24]Krasovskii, N. N.; Lidskii, E. A.: Analytical design of controllers in systems with random attributes, Automat. rem. Control 22, 1021-1025 (1961) · Zbl 0104.36704
[25]Boukas, E. K.: Communications and control engineering, Control of singular systems with random abrupt changes (2008)
[26]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
[27]Souza, C. E.: Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems, IEEE trans. Automat. control 51, No. 5, 836-841 (2006)
[28]X. Li, R. Rakkiyappan, Delay-dependent global asymptotic stability criteria for stochastic genetic regulatory networks with Markovian jumping parameters, Appl. Math. Modell., doi:10.1016/j.apm.2011.09.017, in press.
[29]Shi, P.; Xia, Y.; Liu, G.; Rees, D.: On designing of sliding mode control for stochastic jump systems, IEEE trans. Automat. control 51, No. 1, 97-103 (2006)
[30]Wu, L.; Shi, P.; Gao, H.: State estimation and sliding mode control of Markovian jump singular systems, IEEE trans. Automat. control 55, No. 5, 1213-1219 (2010)
[31]Wang, Z.; Huang, L.; Yang, X.: H performance for a class of uncertain stochastic nonlinear Markovian jump systems with time-varying delay via adaptive control method, Appl. math. Modell. 35, 1983-1993 (2011) · Zbl 1217.93159 · doi:10.1016/j.apm.2010.11.010
[32]Xu, S.; Chen, T.; Lam, J.: Robust H filtering for uncertain Markovian jump systems with mode-dependent time delays, IEEE trans. Automat. control 48, No. 5, 900-907 (2003)
[33]Mahmoud, M. S.; Shi, P.; Ismail, A.: Robust Kalman filtering for discrete-time Markovian jump systems with parameter uncertainty, J. comput. Appl. math. 169, 53-69 (2004) · Zbl 1067.93059 · doi:10.1016/j.cam.2003.11.002
[34]Ma, S.; Boukas, E. K.: Robust H fltering for uncertain discrete Markov jump singular systems with mode-dependent time delay, IET control theory appl. 3, 351-361 (2009)
[35]Boukas, E. K.; Shi, P.: Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters, Int. J. Robust nonlinear control 8, 1155-1167 (1998) · Zbl 0918.93060 · doi:10.1002/(SICI)1099-1239(1998110)8:13<1155::AID-RNC380>3.0.CO;2-F
[36]Qiu, J.; Lu, K.: New robust passive stability criteria for uncertain singularly Markov jump systems with time delays, ICIC express lett. 3, 651-656 (2009)
[37]Yin, Y.; Shi, P.; Liu, F.: Gain scheduled PI tracking control on stochastic nonlinear systems with partially known transition probabilities, J. franklin inst. 348, No. 4, 685-702 (2011) · Zbl 1227.93127 · doi:10.1016/j.jfranklin.2011.01.011
[38]Mao, W.: An LMI approach to D-stability and D-stabilization of linear discrete singular systems with state delay, Appl. math. Comput. 218, No. 5, 1694-1704 (2011)
[39]Xu, S.; Lam, J.: Roubst control filtering of singular systems, (2006)
[40]S. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishnan, Linear matrix inequality in systems and control theory, in: SIAM studies in Applied Mathematics, SIAM, Philadelphia, 1994.