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Volumn 37, Issue 6, 2013, Pages 3748-3760

Observer-based finite-time H∞ control of discrete-time Markovian jump systems

Author keywords

Discrete time systems; Linear matrix inequalities; Markovian jump systems; Stochastic finite time boundedness; Stochastic finite time stabilization

Indexed keywords

CLOSED-LOOP; CONTROL PROBLEMS; DISCRETE TIME SYSTEM; DISCRETE-TIME MARKOVIAN JUMP SYSTEM; FINITE TIME BOUNDEDNESS (FTB); FINITE TIME STABILIZATION; MARKOVIAN JUMP SYSTEMS; SIMULATION EXAMPLE; STATE FEEDBACK CONTROLLER; STATE VECTOR; TIME VARYING;

EID: 84872602133     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2012.07.060     Document Type: Article
Times cited : (44)

References (54)
  • 1
    • 0001682716 scopus 로고
    • Analytical design of controllers in systems with random attributes
    • (1141-1146, 1289-1294)
    • Krassovskii N.N., Lidskii E.A. Analytical design of controllers in systems with random attributes. Automat. Rem. Control 1961, 22:1021-1025. (1141-1146, 1289-1294).
    • (1961) Automat. Rem. Control , vol.22 , pp. 1021-1025
    • Krassovskii, N.N.1    Lidskii, E.A.2
  • 3
    • 33845392294 scopus 로고
    • Stability results for discrete-time linear systems with Markovian jumping parameters
    • Costa O.L.V., Fragoso M.D. Stability results for discrete-time linear systems with Markovian jumping parameters. J. Math. Anal. Appl. 1993, 179(1):154-178.
    • (1993) J. Math. Anal. Appl. , vol.179 , Issue.1 , pp. 154-178
    • Costa, O.L.V.1    Fragoso, M.D.2
  • 4
    • 0003182919 scopus 로고    scopus 로고
    • Stability of stochastic differential equations with Markovian switching
    • Mao X. Stability of stochastic differential equations with Markovian switching. Stoch. Process. Appl. 1999, 79(1):45-67.
    • (1999) Stoch. Process. Appl. , vol.79 , Issue.1 , pp. 45-67
    • Mao, X.1
  • 5
    • 31344474160 scopus 로고    scopus 로고
    • On designing of sliding mode control for stochastic jump systems
    • Shi P., Xia Y., Liu G., Rees D. On designing of sliding mode control for stochastic jump systems. IEEE Trans. Automat. Control 2006, 51(1):97-103.
    • (2006) IEEE Trans. Automat. Control , vol.51 , Issue.1 , pp. 97-103
    • Shi, P.1    Xia, Y.2    Liu, G.3    Rees, D.4
  • 6
    • 77952166462 scopus 로고    scopus 로고
    • State estimation and sliding mode control of Markovian jump singular systems
    • Wu L., Shi P., Gao H. State estimation and sliding mode control of Markovian jump singular systems. IEEE Trans. Automat. Control 2010, 55(5):1213-1219.
    • (2010) IEEE Trans. Automat. Control , vol.55 , Issue.5 , pp. 1213-1219
    • Wu, L.1    Shi, P.2    Gao, H.3
  • 7
    • 0022518706 scopus 로고
    • Discrete-time Markovian-jump linear quadratic optimal-control
    • Chizeck H.J., Willsky A.S., Castanon D. Discrete-time Markovian-jump linear quadratic optimal-control. Int. J. Control 1986, 43(1):213-231.
    • (1986) Int. J. Control , vol.43 , Issue.1 , pp. 213-231
    • Chizeck, H.J.1    Willsky, A.S.2    Castanon, D.3
  • 8
    • 33847367602 scopus 로고    scopus 로고
    • Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems
    • Costa O.L.V., de Paulo W.L. Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems. Automatica 2007, 43(4):587-597.
    • (2007) Automatica , vol.43 , Issue.4 , pp. 587-597
    • Costa, O.L.V.1    de Paulo, W.L.2
  • 9
    • 0038293070 scopus 로고    scopus 로고
    • ∞ filtering for uncertain Markovian jump systems with mode-dependent time delays
    • ∞ filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Trans. Automat. Control 2003, 48(5):900-907.
    • (2003) IEEE Trans. Automat. Control , vol.48 , Issue.5 , pp. 900-907
    • Xu, S.1    Chen, T.2    Lam, J.3
  • 11
    • 79951704915 scopus 로고    scopus 로고
    • ∞ filtering for Markovian jump systems with time-varying delays
    • ∞ filtering for Markovian jump systems with time-varying delays. Int. J. Innov. Comput. Inf. Control 2011, 7(3):1299-1310.
    • (2011) Int. J. Innov. Comput. Inf. Control , vol.7 , Issue.3 , pp. 1299-1310
    • Liu, J.1    Gu, Z.2    Hu, S.3
  • 12
    • 77950163647 scopus 로고    scopus 로고
    • ∞ fault detection filter for Markovian jump linear systems with polytopic uncertainties
    • ∞ fault detection filter for Markovian jump linear systems with polytopic uncertainties. Int. J. Innov. Comput. Inf. Control 2010, 6(3(A)):995-1004.
    • (2010) Int. J. Innov. Comput. Inf. Control , vol.6 , Issue.3 A , pp. 995-1004
    • Ding, Q.1    Zhong, M.2
  • 13
  • 14
    • 78650294207 scopus 로고    scopus 로고
    • ∞ performance for a class of uncertain stochastic nonlinear Markovian jump systems with time-varying delay via adaptive control method
    • ∞ performance for a class of uncertain stochastic nonlinear Markovian jump systems with time-varying delay via adaptive control method. Appl. Math. Model. 2011, 35(4):1983-1993.
    • (2011) Appl. Math. Model. , vol.35 , Issue.4 , pp. 1983-1993
    • Wang, Z.1    Huang, L.2    Yang, X.3
  • 15
    • 0141638538 scopus 로고    scopus 로고
    • A bounded real lemma for jump systems
    • Seiler P., Sengupta R. A bounded real lemma for jump systems. IEEE Trans. Automat. Control 2003, 48(9):1651-1654.
    • (2003) IEEE Trans. Automat. Control , vol.48 , Issue.9 , pp. 1651-1654
    • Seiler, P.1    Sengupta, R.2
  • 16
    • 0033345091 scopus 로고    scopus 로고
    • Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay
    • Shi P., Boukas E.K., Agarwal R.K. Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay. IEEE Trans. Automat. Control 1999, 44(11):2139-2144.
    • (1999) IEEE Trans. Automat. Control , vol.44 , Issue.11 , pp. 2139-2144
    • Shi, P.1    Boukas, E.K.2    Agarwal, R.K.3
  • 17
    • 33646934047 scopus 로고    scopus 로고
    • Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems
    • Souza C.E. Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems. IEEE Trans. Automat. Control 2006, 51(5):836-841.
    • (2006) IEEE Trans. Automat. Control , vol.51 , Issue.5 , pp. 836-841
    • Souza, C.E.1
  • 18
    • 33750432509 scopus 로고    scopus 로고
    • Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems
    • Karan M., Shi P., Kaya C.Y. Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems. Automatica 2006, 42(12):2159-2168.
    • (2006) Automatica , vol.42 , Issue.12 , pp. 2159-2168
    • Karan, M.1    Shi, P.2    Kaya, C.Y.3
  • 19
    • 0032205380 scopus 로고    scopus 로고
    • Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters
    • 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 1998, 8(13):1155-1167.
    • (1998) Int. J. Robust Nonlinear Control , vol.8 , Issue.13 , pp. 1155-1167
    • Boukas, E.K.1    Shi, P.2
  • 20
    • 76549097153 scopus 로고    scopus 로고
    • Stochastic optimal tracking with preview by state feedback for linear discrete-time markovian jump systems
    • Nakura G. Stochastic optimal tracking with preview by state feedback for linear discrete-time markovian jump systems. Int. J. Innov. Comput. Inf. Control 2010, 6(1):15-27.
    • (2010) Int. J. Innov. Comput. Inf. Control , vol.6 , Issue.1 , pp. 15-27
    • Nakura, G.1
  • 21
    • 79953061579 scopus 로고    scopus 로고
    • Gain scheduled PI tracking control on stochastic nonlinear systems with partially known transition probabilities
    • Yin Y., Shi P., Liu F. Gain scheduled PI tracking control on stochastic nonlinear systems with partially known transition probabilities. J. Franklin Inst. 2011, 348(4):685-702.
    • (2011) J. Franklin Inst. , vol.348 , Issue.4 , pp. 685-702
    • Yin, Y.1    Shi, P.2    Liu, F.3
  • 24
    • 0035452456 scopus 로고    scopus 로고
    • Finite-time control of linear systems subject to parametric uncertainties and disturbances
    • Amato F., Ariola M., Dorato P. Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 2001, 37(9):1459-1463.
    • (2001) Automatica , vol.37 , Issue.9 , pp. 1459-1463
    • Amato, F.1    Ariola, M.2    Dorato, P.3
  • 25
    • 0043192304 scopus 로고    scopus 로고
    • Optimal control of non-homogenous prey-predator models during infinite and finite-time intervals
    • EI-Gohary A., AI-Ruzaiza A.S. Optimal control of non-homogenous prey-predator models during infinite and finite-time intervals. Appl. Math. Comput. 2003, 146(2-3):495-508.
    • (2003) Appl. Math. Comput. , vol.146 , Issue.2-3 , pp. 495-508
    • EI-Gohary, A.1    AI-Ruzaiza, A.S.2
  • 26
    • 0037420941 scopus 로고    scopus 로고
    • Optimal control of an angular motion of a rigid body during infinite and finite-time intervals
    • EI-Gohary A. Optimal control of an angular motion of a rigid body during infinite and finite-time intervals. Appl. Math. Comput. 2003, 141(2-3):541-551.
    • (2003) Appl. Math. Comput. , vol.141 , Issue.2-3 , pp. 541-551
    • EI-Gohary, A.1
  • 27
    • 84872598828 scopus 로고
    • Short time stability in linear time-varying systems, in: Proceedings of IRE International Convention Record, Part 4, New York, USA
    • P. Dorato, Short time stability in linear time-varying systems, in: Proceedings of IRE International Convention Record, Part 4, New York, USA, 1961, pp. 83-87.
    • (1961) , pp. 83-87
    • Dorato, P.1
  • 28
    • 0001965541 scopus 로고
    • Finite time stability under perturbing forces and on product spaces
    • Weiss L., Infante E.F. Finite time stability under perturbing forces and on product spaces. IEEE Trans. Automat. Control 1967, 12(1):54-59.
    • (1967) IEEE Trans. Automat. Control , vol.12 , Issue.1 , pp. 54-59
    • Weiss, L.1    Infante, E.F.2
  • 30
    • 14244269055 scopus 로고
    • Finite-time stochastic stability and the analysis of tracking systems
    • Kushner H.J. Finite-time stochastic stability and the analysis of tracking systems. IEEE Trans. Automat. Control 1966, 11(2):219-227.
    • (1966) IEEE Trans. Automat. Control , vol.11 , Issue.2 , pp. 219-227
    • Kushner, H.J.1
  • 31
    • 63649087412 scopus 로고    scopus 로고
    • Finite-time control of linear stochastic systems
    • Zhang W., An X. Finite-time control of linear stochastic systems. Int. J. Innov. Comput. Inf. Control 2008, 4(3):689-696.
    • (2008) Int. J. Innov. Comput. Inf. Control , vol.4 , Issue.3 , pp. 689-696
    • Zhang, W.1    An, X.2
  • 32
    • 65049088106 scopus 로고    scopus 로고
    • Finite-time stability of linear time-varying systems with jumps
    • Amato F., Ambrosino R., Ariola M., Cosentino C. Finite-time stability of linear time-varying systems with jumps. Automatica 2009, 45(5):1354-1358.
    • (2009) Automatica , vol.45 , Issue.5 , pp. 1354-1358
    • Amato, F.1    Ambrosino, R.2    Ariola, M.3    Cosentino, C.4
  • 33
    • 67349250903 scopus 로고    scopus 로고
    • Sufficient conditions for finite-time stability of impulsive dynamical systems
    • Ambrosino R., Calabrese F., Cosentino C., De T.G. Sufficient conditions for finite-time stability of impulsive dynamical systems. IEEE Trans. Automat. Control 2009, 54(4):861-865.
    • (2009) IEEE Trans. Automat. Control , vol.54 , Issue.4 , pp. 861-865
    • Ambrosino, R.1    Calabrese, F.2    Cosentino, C.3    De, T.G.4
  • 34
    • 77950626955 scopus 로고    scopus 로고
    • Finite-time control of discrete-time linear systems: analysis and design conditions
    • Amato F., Ariola M., Cosentino C. Finite-time control of discrete-time linear systems: analysis and design conditions. Automatica 2010, 46(5):919-924.
    • (2010) Automatica , vol.46 , Issue.5 , pp. 919-924
    • Amato, F.1    Ariola, M.2    Cosentino, C.3
  • 35
    • 61349189820 scopus 로고    scopus 로고
    • Finite-time stabilization of linear time-varying continuous systems
    • Garcia G., Tarbouriech S., Bernussou J. Finite-time stabilization of linear time-varying continuous systems. IEEE Trans. Automat. Control 2009, 54(2):364-369.
    • (2009) IEEE Trans. Automat. Control , vol.54 , Issue.2 , pp. 364-369
    • Garcia, G.1    Tarbouriech, S.2    Bernussou, J.3
  • 36
    • 63349101030 scopus 로고    scopus 로고
    • Finite-time stability and stabilization of nonlinear stochastic hybrid systems
    • Yang Y., Li J.M., Chen G.P. Finite-time stability and stabilization of nonlinear stochastic hybrid systems. J. Math. Anal. Appl. 2009, 356(1):338-345.
    • (2009) J. Math. Anal. Appl. , vol.356 , Issue.1 , pp. 338-345
    • Yang, Y.1    Li, J.M.2    Chen, G.P.3
  • 37
    • 80053061477 scopus 로고    scopus 로고
    • Finite-time quantized guaranteed cost fuzzy control for continuous-time nonlinear systems
    • Yang D., Cai K. Finite-time quantized guaranteed cost fuzzy control for continuous-time nonlinear systems. Expert Syst. Appl. 2010, 37(10):6963-6967.
    • (2010) Expert Syst. Appl. , vol.37 , Issue.10 , pp. 6963-6967
    • Yang, D.1    Cai, K.2
  • 38
    • 79951957345 scopus 로고    scopus 로고
    • Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities
    • He S., Liu F. Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities. Appl. Math. Model. 2011, 35(6):2631-2638.
    • (2011) Appl. Math. Model. , vol.35 , Issue.6 , pp. 2631-2638
    • He, S.1    Liu, F.2
  • 39
    • 55549092422 scopus 로고    scopus 로고
    • ∞ control for linear continuous system with norm-bounded disturbance
    • ∞ control for linear continuous system with norm-bounded disturbance. Commun. Nonlinear Sci. Numer. Simul. 2009, 14:1043-1049.
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 1043-1049
    • Meng, Q.1    Shen, Y.2
  • 40
    • 38649137739 scopus 로고    scopus 로고
    • LMI-based finite-time boundedness analysis of neural networks with parametric uncertainties
    • Shen Y., Li C. LMI-based finite-time boundedness analysis of neural networks with parametric uncertainties. Neurocomputing 2008, 71(4-6):502-507.
    • (2008) Neurocomputing , vol.71 , Issue.4-6 , pp. 502-507
    • Shen, Y.1    Li, C.2
  • 41
    • 20344397953 scopus 로고    scopus 로고
    • Finite-time control of discrete-time linear systems
    • Amato F., Ariola M. Finite-time control of discrete-time linear systems. IEEE Trans. Automat. Control 2005, 50(5):724-729.
    • (2005) IEEE Trans. Automat. Control , vol.50 , Issue.5 , pp. 724-729
    • Amato, F.1    Ariola, M.2
  • 42
    • 84859747118 scopus 로고    scopus 로고
    • ∞ finite-time control of discrete-time systems with packet loss
    • 897481
    • ∞ finite-time control of discrete-time systems with packet loss. Math. Probl. Eng. 2012, 2012(897481):1-15.
    • (2012) Math. Probl. Eng. , vol.2012 , pp. 1-15
    • Zhang, Y.1    Cheng, W.2    Mu, X.3    Liu, C.4
  • 43
    • 29244452125 scopus 로고    scopus 로고
    • Finite-time stabilzation via dynamic output feedback
    • Amato F., Ariola M., Dorato P. Finite-time stabilzation via dynamic output feedback. Automatica 2006, 42(2):337-342.
    • (2006) Automatica , vol.42 , Issue.2 , pp. 337-342
    • Amato, F.1    Ariola, M.2    Dorato, P.3
  • 44
    • 83555165153 scopus 로고    scopus 로고
    • ∞ control of singular stochastic systems via static output feedback
    • ∞ control of singular stochastic systems via static output feedback. Appl. Math. Comput. 2012, 218(9):5629-5640.
    • (2012) Appl. Math. Comput. , vol.218 , Issue.9 , pp. 5629-5640
    • Zhang, Y.1    Liu, C.2    Mu, X.3
  • 45
    • 84862784611 scopus 로고    scopus 로고
    • Robust finite-time stabilization of uncertain singular Markovian jump systems
    • Zhang Y., Liu C., Mu X. Robust finite-time stabilization of uncertain singular Markovian jump systems. Appl. Math. Model. 2012, 36(10):5109-5121.
    • (2012) Appl. Math. Model. , vol.36 , Issue.10 , pp. 5109-5121
    • Zhang, Y.1    Liu, C.2    Mu, X.3
  • 46
    • 79551634062 scopus 로고    scopus 로고
    • 2-gain analysis for switched delay systems with norm-bounded disturbance
    • 2-gain analysis for switched delay systems with norm-bounded disturbance. Appl. Math. Comput. 2011, 217(12):5982-5993.
    • (2011) Appl. Math. Comput. , vol.217 , Issue.12 , pp. 5982-5993
    • Lin, X.1    Du, H.2    Li, S.3
  • 48
    • 27844468655 scopus 로고    scopus 로고
    • Static output feedback control for stochastic hybrid systems: LMI approach
    • Boukas E.K. Static output feedback control for stochastic hybrid systems: LMI approach. Automatica 2006, 42(1):183-188.
    • (2006) Automatica , vol.42 , Issue.1 , pp. 183-188
    • Boukas, E.K.1
  • 49
    • 33745969872 scopus 로고    scopus 로고
    • ∞ output dynamic observer-based control of uncertain time-delay systems
    • ∞ output dynamic observer-based control of uncertain time-delay systems. Chaos Solitons Fract. 2007, 31(2):391-403.
    • (2007) Chaos Solitons Fract. , vol.31 , Issue.2 , pp. 391-403
    • Chen, J.1
  • 50
    • 33645835380 scopus 로고    scopus 로고
    • ∞ output feedback stabilization of linear discrete-time systems
    • ∞ output feedback stabilization of linear discrete-time systems. IEEE Trans. Automat. Control 2006, 51(4):675-680.
    • (2006) IEEE Trans. Automat. Control , vol.51 , Issue.4 , pp. 675-680
    • Lee, K.H.1    Lee, J.H.2    Kwon, W.H.3
  • 51
    • 77958002212 scopus 로고    scopus 로고
    • Observer-based finite-time control of time-delayed jump systems
    • He S., Liu F. Observer-based finite-time control of time-delayed jump systems. Appl. Math. Comput. 2010, 217(6):2327-2338.
    • (2010) Appl. Math. Comput. , vol.217 , Issue.6 , pp. 2327-2338
    • He, S.1    Liu, F.2
  • 52
    • 84859988722 scopus 로고    scopus 로고
    • ∞ finite-time control for switched systems with time-varying delay
    • ∞ finite-time control for switched systems with time-varying delay. Nonlinear Anal. Hybrid Syst. 2012, 6(3):885-898.
    • (2012) Nonlinear Anal. Hybrid Syst. , vol.6 , Issue.3 , pp. 885-898
    • Liu, H.1    Shen, Y.2    Zhao, X.3
  • 53
    • 84861015544 scopus 로고    scopus 로고
    • ∞ control of singular Markovian jump systems
    • 205727
    • ∞ control of singular Markovian jump systems. J. Appl. Math. 2012, 2012(205727):1-19.
    • (2012) J. Appl. Math. , vol.2012 , pp. 1-19
    • Zhang, Y.1    Cheng, W.2    Mu, X.3    Guo, X.4
  • 54
    • 0003004622 scopus 로고
    • Linear Matrix Inequality in Systems and Control Theory
    • Society for Industrial and Applied Mathematics, Philadelphia, PA, USA
    • Boyd S., Ghaoui L.E., Feron E., Balakrishnan V. Linear Matrix Inequality in Systems and Control Theory. SIAM Studies in Applied Mathematics 1994, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.
    • (1994) SIAM Studies in Applied Mathematics
    • Boyd, S.1    Ghaoui, L.E.2    Feron, E.3    Balakrishnan, V.4


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