Delay-dependent H∞ control for singular Markovian jump systems with time delay

Optimal Control Applications and Methods

Volumn 30, Issue 5, 2009, Pages 443-461

  Wu, Zhengguang ^a   Su, Hongye ^a   Chu, Jian ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

Delay dependent H control; Linear matrix inequality (LMI); Markovian jumping parameters; Singular time delay systems

Indexed keywords

DELAY-DEPENDENT; EXPLICIT EXPRESSIONS; LINEAR MATRIX INEQUALITY (LMI); LINEAR MATRIX INEQUALITY APPROACH; LMI-CONDITION; MARKOVIAN JUMP SYSTEMS; MARKOVIAN JUMPING PARAMETERS; NUMERICAL EXAMPLE; PERFORMANCE LEVEL; SINGULAR TIME-DELAY SYSTEMS; STATE FEEDBACK CONTROLLER; UPPER BOUND;

CONTROLLERS; FEEDBACK; FEEDBACK CONTROL; FUZZY CONTROL; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; NONLINEAR CONTROL SYSTEMS; NUMERICAL METHODS; STATE FEEDBACK; TIME DELAY;

DELAY CONTROL SYSTEMS;

EID: 70350334658     PISSN: 01432087     EISSN: 10991514     Source Type: Journal    
DOI: 10.1002/oca.860     Document Type: Article

References (32)

1. Shi P, Boukas EK, Agarwal RK. Robust control for Markovian jumping discrete-time systems. International Journal of Systems Science 1999; 30(8):787-797.
2. Boukas EK, Yang H. Exponential stabilizability of stochastic systems with Markovian jumping parameters. Automatica 1999; 35(8):1437-1441.
3. Boukas EK. Stabilization of stochastic nonlinear hybrid systems. International Journal of Innovative Computing, Information and Control 2005; 1(1):131-141.
4. Liu H, Boukas EK, Sun F, Ho DWC. Controller design for Markov jumping systems subject to actuator saturation. Automatica 2006; 35:459-465.
5. Hale J. Functional Differential Equations. Springer: New York, 1977.
6. Niculescu SI, Gu K. Advances in Time-delay Systems. Springer: Germany, 2006.
7. Shi P, Boukas EK, Agarwal RK. Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay. IEEE Transactions on Automatic Control 1999; 44(11):2139-2144. (Pubitemid 30531659)
8. Cao Y, Lam J. Robust H∞ control of uncertain Markovian jump systems with time-delay. IEEE Transactions on Automatic Control 2000; 45(1):77-83.
9. Wang Z, Lam J, Liu X. Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances. IEEE Transactions on Circuits and Systems-II: Express Briefs 2004; 51(5):262-268.
10. Shu Z, Lam J, Xu S. Robust stabilization of Markovian delay systems with delay-dependent exponential estimates. Automatica 2006; 46:2001-2008. (Pubitemid 44436062)
11. Wu J, Chen T, Wang L. Delay-dependent robust stability and H∞ control for jump linear systems with delays. Systems and Control Letters 2006; 55:939-948. (Pubitemid 44344833)
12. Hu L, Shi P, Cao Y. Delay-dependent filtering design for time-delay systems with Markovian jumping parameters. International Journal of Adaptive Control and Signal Processing 2007; 21:434-448.
13. Wei G, Wang Z, Shu H, Fang J. A delay-dependent approach to H∞ filtering for stochastic delayed jumping systems with sensor non-linearities. International Journal of Control 2007; 80(6):885-897.
14. Xu S, Lam J, Mao X. Delay-dependent H∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Transactions on Circuits and Systems-I: Regular Papers 2007; 54(9):2070-2077.
15. Boukas EK, Liu ZK. Deterministic and Stochastic Time Delay Systems. Birkhauser: Boston, 2002.
16. Boukas EK. Stochastic Hybrid Systems: Analysis and Design. Birkhauser: Boston, 2005.
17. Dai L. Singular Control Systems. Springer: Berlin, 1989.
18. Lewis FL. A survey of linear singular systems. Circuits, Systems and Signal Processing 1986; 22(1):3-36.
19. Xu S, Lam J. Robust Control and Filtering of Singular Systems. Springer: Berlin, 2006.
20. Xu S, Dooren PV, Stefan R, Lam J. Robust stability analysis and stabilization for singular systems with state delay and parameter uncertainty. IEEE Transactions on Automatic Control 2002; 47(7):1122-1128. (Pubitemid 34835337)
21. Verghese GC, Levy BC, Kailath T. A generalized state-space for singular systems. IEEE Transactions on Automatic Control 1981; 26(4):811-831.
22. Xu S, Lam J, Yang C. Robust H∞ control for uncertain singular systems with state delay. International Journal of Robust and Nonlinear Control 2003; 13(13):1213-1223.
23. Lam J, Shu Z, Xu S, Boukas EK. Robust H∞ control of descriptor discrete-time Markovian jump systems. International Journal of Control 2007; 80(3):374-385. (Pubitemid 46269099)
24. Boukas EK, Xu S, Lam J. On stability and stabilizability of singular stochastic systems with delays. Journal of Optimization Theory and Applications 2005; 127(2):249-262. (Pubitemid 41705504)
25. Boukas EK, Liu ZK. Delay-dependent stabilization of singularly perturbed jump linear systems. International Journal of Control 2004; 77(3):310-319.
26. Gu K, Kharitonov VL, Chen J. Stability of Time-delay Systems. Birkhauser: Basel, 2003.
27. He Y, Wu M, She J, Liu G. Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Systems and Control Letters 2004; 51(1):57-65.
28. Wu M, He Y, She J, Liu G. Delay-dependent criteria for robust stability of time-varying delay systems. Automatica 2004; 40(8):1435-1439.
29. He Y, Wu M, She J, Liu G. Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Transactions on Automatic Control 2004; 49(5):828-832.
30. He Y, Wang Q, Xie L, Lin C. Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Transactions on Automatic Control 2007; 52(2):293-299.
31. Gao H, Lam J, Chen T, Wang C. Stability analysis of uncertain discrete-time systems with time-varying state delay: A parameter-dependent Lyapunov function approach. Asian Journal of Control 2006; 8:433-440.
32. Zhang X, Wu M, She J, He Y. Delay-dependent stabilization of linear systems with time-varying state and input delays. Automatica 2005; 41:1405-1412. (Pubitemid 40774096)