Robust delay-range-dependent stabilization for Markovian jump systems with mode-dependent time delays and nonlinearities

Optimal Control Applications and Methods

Volumn 31, Issue 3, 2010, Pages 249-264

  Wang, Guoliang ^a,b   Zhang, Qingling ^a,b   Sreeram, Victor ^c  

^a NORTHEASTERN UNIVERSITY   (China)

^b KEY LABORATORY OF INTEGRATED AUTOMATION OF PROCESS INDUSTRY   (China)

^c UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Delay range dependent; Markovian jump systems; Mode dependent time delays; Nonlinear disturbances

Indexed keywords

DELAY-RANGE-DEPENDENT; EXPONENTIAL STABILITY; ILLUSTRATIVE EXAMPLES; LYAPUNOV-KRASOVSKII FUNCTIONALS; MARKOVIAN JUMP SYSTEMS; MEAN-SQUARE; MODE-DEPENDENT TIME DELAYS; NON-LINEARITY; NONLINEAR DISTURBANCE; NONLINEAR PERTURBATIONS; NOVEL TECHNIQUES; ROBUST STABILIZATION PROBLEM; STABILITY CONDITION; STATE FEEDBACK CONTROLLER; SUFFICIENT CONDITIONS; SYSTEM MODE; TIME VARYING;

CONVEX OPTIMIZATION; FEEDBACK; FUZZY CONTROL; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NONLINEAR CONTROL SYSTEMS; NONLINEAR FEEDBACK; STABILIZATION; STATE FEEDBACK; TIME DELAY; UNCERTAIN SYSTEMS;

SYSTEM STABILITY;

EID: 77953112520     PISSN: 01432087     EISSN: 10991514     Source Type: Journal    
DOI: 10.1002/oca.901     Document Type: Article

References (34)

1. Boukas EK, Liu ZK. Robust H∞ control of discrete- time Markovian jump linear systems with mode-dependent time-delays. IEEE Transactions on Automatic Control 2001; 46(12):1918-1924.
2. Xu SY, Lam J. Delay-dependent H∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Transactions on Circuits and Systems 2007 ; 54(9): 2070-2077.
3. Mahmoud MS, Shi P, Boukas EK, Jain L. Simultaneous H2/H∞ control of uncertain jump systems with functional time-delays. International Journal of Robust and Nonlinear Control 2008; 18(3):296-318.
4. Xu SY, Chen TW, Lam J. Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Transactions on Automatic Control 2003; 48(5):900-907.
5. Chen WH, Guan ZH, Yu P. Delay-dependent stability and H∞ control of uncertain discrete-time Markovian jump systems with mode-dependent time delays. Systems and Control Letters 2004; 52(5):361-376.
6. Shao HY. Delay-range-dependent robust H∞ filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters. Journal of Mathematical Analysis and Applications 2008; 342(2):1084-1095.
7. Chen WH, Xu JX, Guan ZH. Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays. IEEE Transactions on Automatic Control 2003; 48(12):2270-2275.
8. Boukas EK, Liu ZK. Output feedback robust stabilization of jump linear systems with mode-dependent time-delays. Proceedings of the American Control Conference, Arlington, 25-27 June 2001; 4683-4688.
9. Sun MH, Lam J, Xu SY, Zou Y. Robust exponential stabilization for Markovian jump systems with mode-dependent input delay. Automatica 2007; 43(10):1799-1807.
10. Wang GL, Zhang QL, Sreeram V. Design of reduced-order H∞ filtering for Markovian jump systems with mode-dependent time delays. Signal Processing 2009 ; 86(2):187-196.
11. Siljak DD, Stipanovic DM. Robust stabilization of nonlinear systems: the LMI appraoch. Mathematical Problems in Engineering 2000; 6(5):461-493.
12. Stipanovic DM, Siljak DD. Robust stability and stabilization of discrete-time nonlinear systems: the LMI approach. International Journal of Control 2001; 74(9):873-879.
13. Zuo ZQ, Wang JZ, Huang L. Robust stabilization for nonlinear discrete-time systems. International Journal of Control 2004; 77(4):384-388.
14. Ho DWC, Lu GP. Robust stabilization for a class of discrete- time non-linear systems via output feedback: the unified LMI approach. International Journal of Control 2003; 76(2): 105-115.
15. Lam J, Gao HJ, Wang CH. Stability analysis for continuous systems with two additive time-varying delay components. Systems and Control Letters 2007; 56(1):16-24.
16. Gao HJ, Chen TW, Lam J. A new delay system approach to network-based control. Automatica 2008; 44(1):39-52.
17. Jiang XF, Han QL, Liu SR, Xue AK. A new H∞ stabilization criterion for networked control systems. IEEE Transactions on Automatic Control 2008; 53(4):1025-1032.
18. Wang ZD, Lam J, Liu XH. Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances. IEEE Transactions on Circuits and Systems 2004; 51(5):262-268.
19. Wei GL, Wang ZD, Shu HS, Fang JA. Robust H∞ control of stochastic time-delay jumping systems with nonlinear disturbances. Optimal Control Applications and Methods 2006; 27(5):255-271.
20. Yue D, Han QL. Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian swithcing. IEEE Transactions on Automatic Control 2005; 50(2):217-222.
21. Mahmoud MS, Shi P. Robust control for Markovian jump linear discrete-time systems with unkown nonlinearities. IEEE Transactions on Automatic Control 2002; 49(4):538-542.
22. Li T, Guo L, Zhang YM. Delay-range-dependent robust stability and stabilization for uncertain systems with time- varying delay. International Journal ofRobust and Nonlinear Control 2008; 18(13):1372-1387.
23. Jiang XF, Han QL. On H∞ control for linear systems with interval time-varying delay. Automatica 2005; 41(12): 2099-2106.
24. He Y, Wang QG, Lin C, Wu M. Delay-range-dependent stability for systems with time-varying delay. Automatica 2007; 43(2):371-376. (Pubitemid 46037586)
25. Shao HY. Improved delay-dependent stability criteria for systems with a delay varying. Automatica 2008; 44(12): 3215-3218.
26. Davis MHA. Markov Models and Optimization. Chapman & Hall: London, U.K., 1993.
27. Mao XR. Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Transactions on Automatic Control 2002; 47(10):1604-1612.
28. Wu J, Chen TW, Wang L. Delay-dependent robust stability and H∞ control for jump linear systems with delays. Systems and Control Letters 2006; 55(11):939-948.
29. Gao HJ, Chen TW. New results on stability of discrete-time systems with time-varying state delay. IEEE Transactions on Automatic Control 2007; 52(2):328-334.
30. Yakukbovich VA. The S-procedure in nonlinear control theory. Vestnik Leningrad University Mathematics 1977; 4:73-93.
31. Boyd S, Ghaoui LE, Feron E, Balakrishnan V. Linear Matrix Inequalities in System and Control Theory.SIAM: Philadelphia, PA, 1994.
32. Wei GL, Wang ZD, Shu HS, Fang JA. 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.
33. Wang ZD, Lam J, Liu XH. Robust filtering for discrete- time Markovian jump delay systems. IEEE Signal Processing Letters 2004; 11(8):659-662.
34. Wang ZD, Qiao H, Burnham KJ. On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters. IEEE Transactions on Automatic Control 2002; 47(4):640-646.