Guaranteed cost control of uncertain discrete-time singular Markov jump systems with indefinite quadratic cost

International Journal of Robust and Nonlinear Control

Volumn 21, Issue 9, 2011, Pages 1031-1045

  Ma, Shuping ^a   Boukas, El Kébir ^b  

^a SHANDONG UNIVERSITY   (China)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

discrete time singular Markov jump system; indefinite quadratic cost; linear matrix inequality (LMI); partially known transition probability; state feedback stabilization

Indexed keywords

INDEFINITE QUADRATIC COST; LINEAR MATRIX INEQUALITY (LMI); PARTIALLY KNOWN TRANSITION PROBABILITY; SINGULAR MARKOV JUMP SYSTEMS; STATE FEEDBACK STABILIZATION;

COST EFFECTIVENESS; COSTS; DELAY CONTROL SYSTEMS; FEEDBACK CONTROL; LINEAR MATRIX INEQUALITIES; NONLINEAR CONTROL SYSTEMS; NUMERICAL METHODS; PROBABILITY; STABILIZATION; STATE FEEDBACK; UNCERTAIN SYSTEMS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 79955631538     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1640     Document Type: Article

References (33)

1. Ji Y, Chizeck HJ, Feng X,. Stability and control of discrete time jump linear-systems. Control Theory and Advanced Technology 1991; 7 (2): 247-270. (Pubitemid 21727532)
2. Xiong J, Lam J, Gao H, Ho DWC,. On robust stabilization of Markovian jump systems with uncertain switching probabilities. Automatica 2005; 41 (5): 897-903. (Pubitemid 40352404)
3. Karan M, Shi P, Kaya CY,. Tranition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems. Automatica 2006; 42 (12): 2159-2168. (Pubitemid 44647194)
4. Boukas EK,. New results on stability and stabilizability of linear systems with random abrupt changes. Les Cahiers du GERAD 2007; G-2007-51.
5. Chizeck HJ, Willsky AS, Castanon D,. Discrete-time Markovian-jump linear quadratic optimal-control. International Journal of Control 1986; 43 (1): 213-231. (Pubitemid 16472738)
6. Costa OLV, Fragoso MD,. Discrete-time LQ-optimal control problems for infinite Markov jump parameter systems. IEEE Transactions on Automatic Control 1995; 40 (12): 2076-2088.
7. Costa OLV, Filho EOA, Boukas EK, Marques RP,. Constrained quadratic control of discrete-time Markovian jump linear systems. Automatica 1999; 35 (4): 617-626.
8. Costa OLV, de Paulo WL,. Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems. Automatica 2007; 43: 587-597. (Pubitemid 46341250)
9. Boukas EK, Swierniak A, Yang H,. On the robustness of jump linear quadratic control. International Journal of Robust and Nonlinear Control 1997; 7 (10): 899-910. (Pubitemid 127664973)
10. Boukas EK, Shi P,. Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters. International Journal of Robust and Nonlinear Control 1998; 8 (13): 1155-1167. (Pubitemid 128632068)
11. â control for discrete-time Markovian jump linear systems with partly unknown transition probabilities. International Journal of Robust and Nonlinear Control 2009; 19 (8): 868-883.
12. Campbell SL,. Singular System of Differential Equations II. Pitman: San Francisco, CA, 1982.
13. Hill DJ, Mareels IMY,. Stability theroy for differential-algebraic systems with application to power sytems. IEEE Transactions on Circuits and Systems 1990; 37 (11): 1416-1423.
14. Luenberger DG, Arbel A,. Singular dynamic leontief systems. Econometrics 1977; 45 (32): 991-995.
15. Aplevich JD,. Implicit Linear Systems. Springer: Berlin, 1991.
16. Dai L,. Singular Control Systems. Lecture Notes in Control and Information Science, vol. 118. Springer: New York, 1989.
17. Boukas EK,. Control of Singular Systems with Random Abrupt Changes. Springer: Berlin, 2008.
18. Cheng Z, Hong H, Zhang J,. The optimal regulation of generalized state-space systems with quadratic cost. Automatica 1988; 24 (5): 697-710.
19. Zhu J, Ma S, Cheng Z,. Singular LQ problem for nonregular descriptor systems. IEEE Transactions on Automatic Control 2002; 47 (7): 1128-1133. (Pubitemid 34835338)
20. Xu S, Lam J,. Robust stability and stabilization of discrete singular systems: an equivalent characterization. IEEE Transactions on Automatic Control 2004; 49 (4): 568-574.
21. Xu S, Lam J,. Robust Control and Filtering of Singular Systems. Springer: Berlin, 2006.
22. Xu S, Song B, Lu J, Lam J,. Robust stability of uncertain discrete-time singular fuzzy systems. Fuzzy Sets and Systems 2007; 158 (20): 2306-2316. (Pubitemid 47238189)
23. â control of descripter discrete time Markovian jump systems. International Journal of Control 2007; 80 (3): 374-385.
24. â control for uncertain discrete-time Markovian jump singular systems. Journal of Control Theory and Applications 2008; 6 (2): 133-140.
25. Xia Y, Zhang J, Boukas EK,. Control for discrete singular hybrid systems. Automatica 2008; 48: 2635-2641.
26. Zhou W, Lu H, Duan C, Li M,. Delay-dependent robust control for singular discrete-time Markovian jump systems with time-varying delay. International Journal of Robust and Nonlinear Control 2010; 20 (10): 1112-1128.
27. Boukas EK,. Static output feedback control for stochastic hybrid systems: LMI approach. Automatica 2006; 42 (1): 183-188. (Pubitemid 41660576)
28. Lu H, Zhou W, Li M,. Guaranteed cost control for uncertain singular system with Markovian jumping parameters. The Seventh World Congress on Intelligent Control and Automation, Chongqing, China, 2008; 7198-7203.
29. Chen S, Zhou X,. Stochastic linear quadratic regulators with indefinite control weight costs. SIAM Journal on Control and Optimization 2002; 39: 1065-1081.
30. Liu YJ, Zhou XY,. Near-optimal controls of random-switching LQ problems with indefinite control weight costs. Automatica 2005; 41 (6): 1063-1070. (Pubitemid 40556816)
31. â control for linear systems with norm-bounded time-varying uncertainty. IEEE Transactions on Automatic Control 1992; 37 (8): 1188-1191.
32. Petersen IR,. A stabilization algorithm for a class of uncertain linear systems. Systems Control Letters 1987; 8 (4): 351-357.
33. Fridman E, Shaked U,. An improved stabilization method for linear time-delay systems. IEEE Transactions on Automatic Control 2002; 47 (11): 1931-1937. (Pubitemid 35426901)