Delay-dependent BIBO stability analysis of switched uncertain neutral systems

Mathematical and Computer Modelling

Volumn 53, Issue 9-10, 2011, Pages 1607-1620

  Xiong, Liang Lin ^a   Zhong, Shou Ming ^b   Ye, Mao ^b  

^a YUNNAN MINZU UNIVERSITY   (China)

^b UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Delay dependent BIBO stability; Lyapunov Metzler LMIs; State dependent switching rule; Switched neutral systems; Variation of constants formula

Indexed keywords

BIBO STABILITY; LYAPUNOV-METZLER LMIS; NEUTRAL SYSTEMS; STATE-DEPENDENT; VARIATION-OF-CONSTANTS FORMULA;

FEEDBACK; LINEAR MATRIX INEQUALITIES; STATE FEEDBACK; SWITCHING; SWITCHING SYSTEMS; SYSTEM STABILITY; UNCERTAIN SYSTEMS;

STABILITY CRITERIA;

EID: 79951951824     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2010.12.026     Document Type: Article

References (41)

1. Sun Z., Ge S.-S. Analysis and synthesis of switched linear control systems. Automatica 2005, 41:181-195.
2. Sun Z.-D. Stabilizability and insensitivity of switched linear systems. IEEE Transactions on Automatic Control 2004, 49:1133-1137.
3. Kim S., Campbell S.-A., Liu X. Stability of a class of linear switching systems with time delay. IEEE Transactions on Circuits and Systems I 2006, 53:384-393.
4. Du D.-S., Jiang B., Shi P., Zhou S.-S. Robust l2-l∞ control for uncertain discrete-time switched systems with delays. Circuits, Systems, and Signal Processing 2006, 25:729-744.
5. Hu K., Yuan J. Improved robust H∞ filtering for uncertain discrete-time switched systems. IET Control Theory & Applications 2009, 3:315-324.
6. Sun X.-M., Zhao J., Hill D.J. Stability and L2-gain analysis for switched delay systems: A delay-dependent method. Automatica 2006, 42:1769-1774.
7. Liberzon D. Switching in Systems and Control 2003, Birkhauser, Boston.
8. Zhai G.-S., Xu X.-P., Lin H., Michel A.N. Analysis and design of switched normal systems. Nonlinear Analysis: Theory, Methods & Applications 2006, 65:2248-2259.
9. Li R., Teo K.L., Wong K.H., Duan G.R. Control parameterization enhancing transform for optimal control of switched systems. Mathematical and Computer Modelling 2006, 43:1393-1403.
10. Alwan Mohamad S., Liu X.-Z. On stability of linear and weakly nonlinear switched systems with time delay. Mathematical and Computer Modelling 2008, 48:1150-1157.
11. Liu Y.-B., Feng W.-Z. Razumikhin-Lyapunov functional method for the stability of impulsive switched systems with time delay. Mathematical and Computer Modelling 2009, 49:249-264.
12. Xu H.-L., Liu X.-Z, Teo K.L. Robust H∞ stabilization with definite attendance of uncertain impulsive switched systems. Journal of ANZIAM 2005, 46:471-484.
13. Xu H.-L., Teo K.L. Robust stabilization of uncertain impulsive switched systems with delayed control. Computers & Mathematics with Applications 2008, 56:63-70.
14. Xu H.-L., Teo K.L., Liu X. Robust stability analysis of guaranteed cost control for impulsive switched systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 2008, 38:1419-1422.
15. Xu H.-L., Teo K.L. H∞ optimal stabilization of a class of uncertain impulsive systems: an LMI approach. Journal of Industrial and Management Optimization 2009, 5:153-159.
16. Xu H.-L., Liu X.-Z., Teo K.-L. Delay independent stability criteria of impulsive switched systems with time-invariant delays. Mathematical and Computer Modelling 2008, 47:372-379.
17. Lin H., ANTSAKLIS P.-J. Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Transactions on Automatic Control 2009, 54:308-322.
18. Wu H., Mizukami K. Robust stabilization of uncertain linear dynamical systems. International Journal of Systems Science 1993, 24:265-276.
19. Xu D.-Y., Zhong S.-M., Li M. BIBO stabilization of large-scale systems. Control Theory and Applications 1995, 12:758-763.
20. Xu D.-Y., Zhong S.-M. Robust BIBO stabilization of linear large-scale systems with nonlinear delay perturbations, dynamics of continuous. Discrete and Impulsive Systems 1996, 2:511-520.
21. Fu Y.-L., Liao X.-X. BIBO stabilization of stochastic delay systems with uncertainty. IEEE Transactions on Automatic Control 2003, 48:133-138.
22. Li P., Zhong S.-M. BIBO stabilization of time-delayed system with nonlinear perturbation. Applied Mathematics and Computation 2008, 195:264-269.
23. Li P., Zhong S.-M. BIBO stabilization for system with multiple mixed delays and nonlinear perturbations. Applied Mathematics and Computation 2008, 196:207-213.
24. Li P., Zhong S.-M. BIBO stabilization of piecewise switched linear systems with delays and nonlinear perturbations. Applied Mathematics and Computation 2009, 213:405-410.
25. Li P., Zhong S.-M., Cui J.-Z. Stability analysis of linear switching systems with time delays. Chaos, Solitons & Fractals 2009, 40:474-480.
26. Han Q.-L. A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays. Automatica 2004, 40:1791-1796.
27. Xiong L.-L., Zhong S.-M., Tian J.-K. Novel robust stability criteria of uncertain neutral systems with discrete and distributed delays. Chaos, Solitons & Fractals 2009, 40:771-777.
28. Sun X.-M., Fu J., Sun H.-F., Zhao J. Stability of linear switched neutral delay systems. Proceedings of The Chinese Society for Electrical Engineering 2005, 25:42-46.
29. Zhang Y., Liu X., Zhu H. Stability analysis and control synthesis for a class of switched neutral systems. Applied Mathematics and Computation 2007, 190:1258-1266.
30. Liu D.-Y., Liu X.-Z., Zhong S.-M. Delay-dependent robust stability and control synthesis for uncertain switched neutral systems with mixed delays. Applied Mathematics and Computation 2008, 205:828-839.
31. Geromel J.-C., Colaneri P. Stability and stabilization of continuous-time switched linear systems. SIAM Journal on Control and Optimization 2006, 45:1915-1930.
32. Michaletzky Gyorgy, Gerencser Laszlo BIBO stability of linear switching systems. IEEE Transactions on Automatic Control 2002, 47:1895-1898.
33. Partington Jonathan R., Bonnet Catherine H∞ and BIBO stabilization of delay systems of neutral type. Systems & Control Letters 2004, 52:283-288.
34. Du D.-S., Jiang B., Shi P., Zhou S.-S. Robust l2-l∞ control for uncertain discrete-time switched systems with delays. Circuits, Systems, and Signal Processing 2006, 25(June):729-744.
35. Zhou S.-S., Lam J. Robust stabilization of delayed singular systems with linear fractional parametric uncertainties. Circuits, Systems and Signal Processing 2003, 22:579-588.
36. Hale J.-K. Theory of Functional Differential Equations 1977, Springer-Verlag.
37. Rockafellar R. Convex Analysis 1970, Princeton Press, Princeton, NJ.
38. Garg K.-M. Theory of Differentiation: A Unified Theory of Differentiation via New Derivate Theorems and New Derivatives 1998, Wiley-Interscience, New York.
39. Lasdon L.-S. Optimization Theory for Large Scale Systems. Series of Operation Research 1970, MacMillan, New York.
40. K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, December 2000, pp. 2805-2810.
41. Moon Y.-S., Park P., Kwon W.-H., Lee Y.-S. Delay-dependent robust stabilization of uncertain state-delayed systems. International Journal of Control 2001, 74:1447-1455.