Delay-dependent stability and stabilization of uncertain discrete-time markovian jump singular systems with time delay

ANZIAM Journal

Volumn 49, Issue 1, 2008, Pages 111-129

  Ma, Shuping ^a   Liu, Xinzhi ^a,b   Zhang, Chenghui ^a  

^a SHANDONG UNIVERSITY   (China)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

delaydependent; discrete Markovian jump singular system; linear matrix inequality (LMI); robust stochastic stability and stabilization.; time delay system

Indexed keywords

EID: 61849156567     PISSN: 14461811     EISSN: 14468735     Source Type: Journal    
DOI: 10.1017/S1446181100012712     Document Type: Article

References (24)

1. Aplevich J.D. Implicit Linear Systems 1991 Springer-Verlag, Berlin
2. E. K. Boukas, "Static output feedback control for stochastic hybrid systems: LMI approach", Automatica J. IPAC 42 (2006) 183-188. (Pubitemid 41660576)
3. E. K. Boukas and N. F. Al-Muthairi, "Delay-dependent stabilization of singular linear systems with delays", Int. J. Innovative Comput. Information Contr. 2 (2006) 283-291.
4. ∞ control of discrete-time jump linear systems with time-delays: an LMI approach", in Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 1999), 1527-1532.
5. ∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays", IEEE Trans. Automat. Contr. 46 (2001) 1918-1924.
6. ∞ control for discrete-time jump linear systems with time delay", J. Franklin Inst. 336 (1999) 1263-1281.
7. B. Chen, J. Lam and S. Xu, "Memory state feedback guaranteed cost control for neutral delay systems", Int. J. Innovative Comput. Information Contr. 2 (2006) 293-303.
8. ∞ control of uncertain discrete-time Markovian jump systems with mode-dependent time delays", Systems Control Lett. 52 (2004) 361-376.
9. L. Dai, Singular Control Systems. Lecture Notes in Control and Information Sciences (SpringerVerlag, New York, 1989).
10. ∞ control of linear time-delay systems", IEEE Trans. Automat. Contr. 47 (2002) 253-270.
11. E. Fridman and U. Shaked, "An improved stabilization method for linear time-delay systems", IEEE Trans. Automat. Contr. 47 (2002) 1931-1937. (Pubitemid 35426901)
12. Y. He, M. Wu, J. H. She and G. P. Liu, "Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays", Systems Control Lett. 51 (2004) 57-65.
13. Y. He, M. Wu, J. H. She and G. P. Liu, "Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic type uncertainties", IEEE Trans. Automat. Contr. 49 (2004) 828-832.
14. S. P. Ma and Z. L. Cheng, "An LMI approach to robust stabilization for uncertain discrete-time singular systems", in Proceedings of the 41st IEEE CDC, Las Vegas, Nevada, USA, 2002), 1090-1095.
15. S. P. Ma and Z. L. Cheng, "Delay-dependent robust stabilization for uncertain discrete-time singular systems with time-delay", in Proceedings of the Sixth World Congress on Intelligent Control and Automation, Dalian, China, 2006), 2081-2085. (Pubitemid 46533145)
16. I.R. Petersen, "A stabilization algorithm for a class of uncertain linear systems", Systems Control Lett. 8 (1987) 351-357. (Pubitemid 17589056)
17. ∞ control design for singular continuous-time delay systems with parametric uncertainties", Nonlinear Dyn. Syst. Theory 4 (2004) 59-71.
18. P. Shi, E. K. Boukas and K. Agarwal, "Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay", IEEE Trans. Automat. Contr. 44 (1999) 2139-2144. (Pubitemid 30531659)
19. M. Wu, Y. He and J. H. She, "New delay-dependent stability criteria and stabilizing method for neutral systems", IEEE Trans. Automat. Contr. 49 (2004) 2266-2271. (Pubitemid 40043332)
20. M. Wu, Y. He, J. H. She and G. P. Liu, "Delay-dependent criteria for robust stability of time-varying delay systems", Automatica J. IPAC 40 (2004) 1435-1439.
21. S. Xu, P. V. Dooren, R. Stefan and J. Lam, "Robust stability and stabilization for singular systems with state delay and parameter uncertainty", IEEE Trans. Automat. Contr. 47 (2002) 1122-1128. (Pubitemid 34835337)
22. S. Xu and J. Lam, "Robust stability and stabilization of discrete singular systems: An equivalent characterization", IEEE Trans. Automat. Contr. 49 (2004) 568-574.
23. ∞ control for discrete singular systems with state delay and parameter uncertainty", Dyn. Contin. Discrete Impuls. Syst Ser. B Appl. Algorithms 9 (2002) 539-554.
24. ∞ control of uncertain descriptor systems with multiple delays", IEE Proceedings - Control Theory and Applications 150 (2003) 557-564.