Robust exponential stability of uncertain singular Markovian jump time-delay systems

Zidonghua Xuebao/ Acta Automatica Sinica

Volumn 36, Issue 4, 2010, Pages 558-563

  Wu, Zheng Guang ^a   Su, Hong Ye ^a   Chu, Jian ^a  

^a STATE KEY LABORATORY OF INDUSTRIAL CONTROL TECHNOLOGY   (China)

Author keywords

Exponential stability; Linear matrix inequality (LMI); Markovian jumping parameters; Singular systems; Time delay

Indexed keywords

DELAY-DEPENDENT; DELAY-RANGE-DEPENDENT; EXPONENTIAL STABILITY; EXPONENTIALLY STABLE; LINEAR MATRIX INEQUALITY APPROACH; MARKOVIAN JUMP SYSTEMS; MARKOVIAN JUMPING PARAMETERS; MARKOVIAN JUMPS; MEAN-SQUARE; NOMINAL SYSTEM; NUMERICAL EXAMPLE; ROBUST EXPONENTIAL STABILITY; SINGULAR SYSTEM; SINGULAR SYSTEMS; TIME-DELAY SYSTEMS;

DELAY CONTROL SYSTEMS; EXPONENTIAL FUNCTIONS; FUZZY CONTROL; LINEAR MATRIX INEQUALITIES; TIME DELAY;

SYSTEM STABILITY;

EID: 77952611227     PISSN: 02544156     EISSN: None     Source Type: Journal    
DOI: 10.3724/SP.J.1004.2010.00558     Document Type: Article

References (30)

1. Dai L. Singular Control Systems. Berlin: Springer, 1989
2. Xu S Y, Lam J. Robust Control and Filtering of Singular Systems. Berlin: Springer, 2006
3. Lewis F L. A survey of linear singular systems. Circuits, Systems and Signal Processing, 1986, 5(1): 3-36
4. Xu S Y, Lam J, Zou Y. An improved characterization of bounded realness for singular delay systems and its applications. International Journal of Robust and Nonlinear Control, 2008, 18(3): 263-277
5. Xu S Y, Dooren P V, Stefan R, Lam J. Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Transactions on Automatic Control, 2002, 47(7): 1122-1128
6. ∞ controller design for uncertain descriptor systems with time-varying discrete and distributed delays. IEE Proceedings-Control Theory and Applications, 2005, 152(6): 628-638
7. Yue D, Lam J, Ho D W C. Delay-dependent robust exponential stability of uncertain descriptor systems with time-varying delays. Dynamics of Continuous, Discrete and Impulsive Systems B: Applications and Algorithms, 2005, 12(1): 129-149
8. Zhu S Q, Zhang C H, Cheng Z L, Feng J. Delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems. IEEE Transactions on Automatic Control, 2007, 52(5): 880-885
9. Ma S, Cheng Z, Zhang C. Delay-dependent robust stability and stabilization for uncertain discrete singular systems with time-varying delays. IET Control Theory and Applications, 2007, 1(4): 1086-1095
10. ∞control for uncertain discrete-time singular systems with time-delays. Journal of Computational and Applied Mathematics, 2008, 217(1): 194-211
11. Su H Y, Ji X F, Chu J. Delay-dependent robust control for uncertain singular time-delay systems. Asian Journal of Control, 2006, 8(2): 180-189
12. Boukas E K. Stochastic Hybrid Systems: Analysis and Design. Boston: Birkhauser, 2005
13. Mao X R, Yuan C G. Stochastic Differential Equations with Markovian Switching. UK: Imperial College Press, 2006
14. Ma S P, Liu X Z, Zhang C H. Delay-dependent stability and stabilization of uncertain discrete-time Markovian jump singular systems with time delay. ANZIAM Journal, 2007, 49(1): 111-129
15. ∞control for uncertain discrete Markovian jump singular systems with mode-dependent time-delay. International Journal of Robust and Nonlinear Control, 2008, 19(9): 965-985
16. Boukas E K, Xu S Y, Lam J. On stability and stabilizability of singular stochastic systems with delays. Journal of Optimization Theory and Applications, 2005, 127(2): 249-262
17. Boukas E K, Liu Z K. Delay-dependent stabilization of singularly perturbed jump linear systems. International Journal of Control, 2004, 77(3): 310-319
18. ∞ control for singular Markovian jump systems with time delay. Optimal Control Application and Methods, 2008, 30(5): 443-461
19. Wu M, He Y, She J G, Liu G P. Delay-dependent criteria for robust stability of time-varying delay systems. Automatica, 2004, 40(8): 1435-1439
20. He Y, Wu M, She J G, Liu G P. Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Systems and Control Letters, 2004, 51(1): 57-65
21. He Y, Wu M, Liu G P, She J H. Output feedback stabilization for a discrete-time system with a time-varying delay. IEEE Transactions on Automatic Control, 2008, 53(10): 2372-2377
22. He Y, Wang Q G, Xie L H, 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
23. He Y, Wang Q G, Lin C, Wu M. Delay-range-dependent stability for systems with time-varying delay. Automatica, 2007, 43(2): 371-376
24. Xu S Y, Lam J. On equivalence and efficiency of certain stability criteria for time-delay systems. IEEE Transactions on Automatic Control, 2007, 52(1): 95-101
25. Peng C, Tian Y. Delay-dependent robust stability criteria for uncertain systems with interval time varying delay. Journal of Computational and Applied Mathematics, 2008, 214(2): 480-494
26. ∞ filter design of uncertain descriptor systems with discrete and distributed delays. IEEE Transactions on Signal Processing, 2004, 52(11): 3200-3212
27. Petersen I R. A stabilization algorithm for a class of uncertain linear systems. Systems and Control Letters, 1987, 8(4): 351-357
28. ∞control of jump linear systems with time-delay. International Journal of Control, 2001, 74(4): 329-340
29. Gu K, Kharitonov V L, Chen J. Stability of Time-Delay Systems. Boston: Birkhauser, 2003
30. Mao X, Koroleva N, Rodkina A. Robust stability of uncertain stochastic differential delay equations. Systems and Control Letters, 1998, 35(5): 325-336