Absolute stability criteria for a class of nonlinear singular systems with time delay

Nonlinear Analysis, Theory, Methods and Applications

Volumn 70, Issue 2, 2009, Pages 621-630

  Wang, Huijiao ^a,b   Xue, Anke ^c   Lu, Renquan ^c  

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

^b ZHEJIANG SCI TECH UNIVERSITY   (China)

^c HANGZHOU DIANZI UNIVERSITY   (China)

Author keywords

Absolute stability; Linear matrix inequality (LMI); Nonlinear singular systems; Sector bounded nonlinearity; Time delay

Indexed keywords

CONTROL THEORY; DELAY CONTROL SYSTEMS; FUZZY CONTROL; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; SYSTEM STABILITY; TIME DELAY; UNCERTAIN SYSTEMS;

ABSOLUTE STABILITIES; ABSOLUTE STABILITY; ABSOLUTE STABILITY CRITERIONS; BOUNDING TECHNIQUES; DELAY INDEPENDENTS; DELAY-DEPENDENT CRITERION; LINEAR MATRIX INEQUALITY (LMI); LINEAR MATRIXES; MODEL TRANSFORMATIONS; NON LINEARITIES; NONLINEAR SINGULAR SYSTEMS; NUMERICAL EXAMPLES; SECTOR-BOUNDED NONLINEARITY; SINGULAR SYSTEMS; SLACK VARIABLES; TIME- DELAYS;

STABILITY CRITERIA;

EID: 56049125474     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.12.030     Document Type: Article

References (36)

1. Lur'e A.I. Some Nonlinear Problem in the Theory of Automatic Control (1957), H.M. Stationary Office, London
2. Bliman P.-A. Lyapunov-Krasovskii functionals and frequency domain: Delay-independent absolute stability criteria for delay systems. International Journal of Robust and Nonlinear Control 11 (2001) 771-788
3. Gan Z.X., and Ge W.G. Lyapunov functional for multiple delay general Lur'e control systems with multiple nonlinearities. Journal of Mathematics Analysis and Applications 256 (2001) 596-608
4. He Y., and Wu M. Absolute stability for multiple delay general Lur'e control systems with multiple nonlinearities. Journal of Computational and Applied Mathematics 159 (2003) 241-248
5. L. Yu, Q.-L. Han, S. Yu, F. Gao, Delay-dependent conditions for robust absolute stability of uncertain time-delay systems, in: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, USA, 2003, pp. 6033-6037
6. Han Q.-L. Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica 41 (2005) 2171-2176
7. Han Q.-L., and Yue D. Absolute stability of Lur'e systems with time-varying delay. IET Control Theory Applications 1 (2007) 854-859
8. Han Q.-L. A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems. Automatica 41 (2007) 10.1016/j.automatica.2007.04.009
9. Q.-L. Han, A. Xue, S. Liu, X. Yu, Robust absolute stability criteria for uncertain Lur'e systems of neutral type, International Journal of Robust and Nonlinear Control, doi.10.1002/rnc.1219
10. Y. Wang, Z. Zuo, G. Zhang, New absolute stability condition for time-delay systems with sector-bounded nonlinearity, in: Proceedings of the 2007 American Control Conference, New York City, USA, 2007, pp. 6027-6030
11. He Y., Wu M., She J.-H., and Liu G.-P. Robust stability for delay Lurie control systems with multiple nonlinearities. Journal of Computational and Applied Mathematics 176 (2005) 371-380
12. He Y., Wang Q.-G., Xie L., and Lin C. Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Transactions on Automatic Control 52 (2007) 293-299
13. J. Gao, H. Su, X. Ji, J. Chu, Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity, Nonlinear Analysis: Real World Applications (2007), in press (doi:10.1016/j.nonrwa.2007.07.003)
14. Xu S., and Lam J. On equivalence and efficiency of certain stability criteria for time-delay systems. IEEE Transactions on Automatic Control 52 (2007) 95-101
15. Dai L. Singular Control Systems (1989), Springer-Verlag, Berlin, Germany
16. Lewis F.L. A survey of linear singular systems. Circuits, Systems Signal Processing 5 (1986) 3-36
17. Xu S., Dooren P.V., Stefan R., and Lam J. Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Transactions on Automatic Control 47 (2002) 1122-1128
18. ∞ control for discrete singular systems with parameter uncertainties. Acta Automatica Sinica 33 (2007) 1299-1304
19. Zhou S., and Lam J. Robust stabilization of delayed singular systems with linear fractional parametric uncertainties. Circuits, Systems Signal Processing 6 (2003) 579-588
20. Lee L., and Chen J.L. Strict positive real lemma and absolute stability for discrete-time descriptor systems. IEEE Transactions on Circuits and Systems-I 50 (2003) 788-794
21. Yang C., Zhang Q., and Zhou L. Generalised absolute stability analysis and synthesis for Lur'e-type descriptor systems. IET Control Theory Applications 1 (2007) 617-623
22. Gu K., and Niculescu S.-I. Additional dynamics in transformed time-delay systems. IEEE Transactions on Automatic Control 45 (2000) 572-575
23. Khalil H.K. Nonlinear Systems (1996), Prentice Hall, Upper Saddle River, NJ
24. Kristic M., and Deng H. Stabilization of Nonlinear Uncertain Systems (1998), Springer-Verlag, London, UK
25. Boyd S., and Ghaoui L.E. Linear Matrix Inequalities in System and Control Theory (1994), SIAM, Philadelphia
26. Petersen I.R. A stabilization algorithm for a class of uncertain linear systems. Systems & Control Letters 8 (1987) 351-357
27. Han Q.-L., Yu X., and Gu K. On computing the maximum time-delay bound for stability of linear neutral systems. IEEE Transactions on Automatic Control 49 (2004) 2281-2286
28. Han Q.-L. On stability of linear neutral systems with mixed time-delays: A discretized Lyapunov functional approach. Automatica 41 (2005) 1209-1218
29. Han Q.-L. On designing time-varying delay feedback controller for master-slave synchronization of Lur'e systems. IEEE Transactions on Circuits and Systems-I: Regular Papers 54 (2007) 1573-1583
30. Han Q.-L. New delay-dependent synchronization criteria for Lur'e systems using time delay feedback control. Physics Letters A 360 (2007) 563-569
31. S.Q. Zhu, Z.L. Chen, J. Feng, Delay-dependent robust stability criterion and robust stabilization for uncertain singular time-delay systems, in: Proceeding of American Control Conference, Portland, USA, 2005, pp. 2839-2844
32. ∞ control for linear descriptor systems with delay in state. Journal of Control Theory and Application 3 (2005) 76-84
33. Zhong R., and Yang Z. Delay-dependent robust control of descriptor systems with time delay. Asian Journal of Control 8 (2006) 36-44
34. Gao H.L., Zhu S.Q., Chen Z.L., and Xu B.G. Delay-dependent state feedback guaranteed cost control uncertain singular time-delay systems. Proceeding of IEEE Conference on Decision and Control, and European Control Conference (2003), IEEE 4354-4359
35. ∞ control of linear state-delay descriptor systems: An LMI approach. Linear Algebra and its Applications 351 (2002) 271-302
36. Wu Z.G., and Zhou W.N. Delay-dependent robust stabilization for uncertain singular systems with state delay. Acta Automatica Sinica 33 (2007) 714-718