Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters

Applied Mathematics and Computation

Volumn 216, Issue 11, 2010, Pages 3396-3407

  Balasubramaniam, P ^a   Manivannan, A ^a   Rakkiyappan, R ^a  

^a GANDHIGRAM RURAL UNIVERSITY   (India)

Author keywords

Generalized eigenvalue problems; Global exponential stability; Linear matrix inequality; Lyapunov Krasovskii functional; Markovian jumping parameters

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; MATRIX ALGEBRA; NUMERICAL METHODS; ROBUSTNESS (CONTROL SYSTEMS); STABILITY; SYSTEM STABILITY; TIME DELAY; TIME VARYING CONTROL SYSTEMS; UNCERTAIN SYSTEMS; UNCERTAINTY ANALYSIS;

GENERALIZED EIGENVALUE PROBLEMS; GLOBAL EXPONENTIAL STABILITY; INTERVAL TIME-VARYING DELAYS; LOWER AND UPPER BOUNDS; LYAPUNOV-KRASOVSKII FUNCTIONALS; MARKOVIAN JUMPING PARAMETERS; TIME VARYING- DELAYS; UNCERTAIN NEUTRAL SYSTEMS;

STABILITY CRITERIA;

EID: 84856276585     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.04.077     Document Type: Article

References (34)

1. W. P. Blair, D. D. Sworder, Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria, International Journal of Control 21(1975) 833-841.
2. D. D. Sworder, R. O. Rogers, An LQG solution to a control problem with solar thermal receiver, IEEE Transactions on Automatic Control 28(1983) 971-978.
3. M. Athans, Command and control (C2) theroy: a challenge to control science, IEEE Transactions on Automatic Control 32(1987) 286-293. (Pubitemid 17548870)
4. J. K. Hale, S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, New York, 1993.
5. C. H. Lien, J. D. Chen, Discrete-delay-independent, discrete-delay- dependent criteria for a class of neutral systems, Journal of Dynamic Systems, Measurement and Control 125(2003) 33-41.
6. J. H. Park, Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations, Applied Mathematics and Computation 161(2005) 413-421.
7. J. H. Park, Robust stabilization for dynamic systems with multiple time-varying delays and nonlinear uncertainties, Journal of Optimization Theory and Applications 108(2001) 155-174.
8. O. M. Kwon, J. H. Park, Delay-range-dependent stabilization of uncertain dynamic systems with interval time-varying delays, Applied Mathematics and Computation 208(2009) 58-68.
9. O. M. Kwon, J. H. Park, S. M. Lee, On robust stability for uncertain neural networks with interval time-varying delays, IET Control Theory and Applications 2(2008) 625-634.
10. Q. L. Han, On stability of linear neutral systems with mixed time delays: a discretized Lyapunov functional approach, Automatica 41(2005) 1209-1218.
11. J. H. Park, Stability criterion for neutral differential systems with mixed multiple time-varying delay arguments, Mathematics and Computers in Simulation 59(2002) 401-412. (Pubitemid 34545695)
12. Q. L. Han, A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices, International Journal of Systems Science 36(2005) 469-475.
13. Y. He, M. Wu, J. H. She, G. P. Liu, Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems and Control Letters 51(2004) 57-65.
14. S. Xu, J. Lam, Y. Zou, Further results on delay-dependent robust stability conditions of uncertain neutral systems, International Journal of Robust and Nonlinear Control 15(2005) 233-246. (Pubitemid 40384289)
15. S. Xu, J. Lam, A survey of linear matrix inequality techniques in stability analysis of delay systems, International Journal of Systems Science 39(2008) 1095-1113.
16. S. Xu, G. Feng, Improved robust absolute stability criteria for uncertain time-delay systems, IET Control Theory and Applications 1(2007) 1630-1637. (Pubitemid 350136749)
17. Y. He, Q. G. Wang, C. Lin, M. Wu, Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems, International Journal of Robust and Nonlinear Control 15(2005) 923-933. (Pubitemid 41815801)
18. K. W. Yu, C. H. Lien, Stability criteria for uncertain neutral systems with interval time-varying delays, Chaos, Solitons, Fractals 38(2008) 650-657.
19. M. N. A. Parlakci, Delay-dependent robust stability criteria for uncertain neutral systems with mixed time-varying discrete and neutral delays, Asian Journal of Control 9(2008) 411-421.
20. J. Zhang, P. Shi, J. Qiu, Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties, Chaos, Solitons, Fractals 38(2008) 160-167. (Pubitemid 351503978)
21. M. Liu, Stability analysis of neutral-type nonlinear delayed systems: an LMI approach, Journal of Zhejiang University Science 7(2006) 237-244. (Pubitemid 44347952)
22. C. C. Shen, S. M. Zhong, New delay-dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties, Chaos, Solitons, Fractals 40(2009) 2277-2285.
23. H. R. Karimi, M. Zapateiro, N. Luo, Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties, Chaos, Solitons, Fractals 42(2009) 595-603.
24. N. N. Krasovskii, E. A. Lidskii, Analysis design of controller in systems with random attributes, Part I, Automatic Remote Control 22(1961) 1021-1025.
25. X. M. Sun, J. Zhao, D. J. Hill, Stability and gain analysis for switched delay systems: a delay-dependent method, Automatica 42(2006) 1769-1774. (Pubitemid 44277968)
26. X. M. Sun, W. Wang, J. Zhao, Stability analysis for linear switched systems with time-varying delay, IEEE Transactions on System Man Cybernetics B 38(2008) 528-533. (Pubitemid 351479570)
27. 1 control and filtering for uncertain markovian Jump systems with time-varying delays, IEEE Transactions on Circuits and Systems-I: Regular Papers 54(2007) 2070-2077. (Pubitemid 47456047)
28. M. Mariton, Jump Linear Systems in Automatic Control, Dekker, New York, 1990.
29. B. Chen, H. Li, P. Shi, C. Lin, Q. Zhou, Delay-dependent stability analysis and controller synthesis for Markovian jump systems with state and input delays, Information Sciences 179(2009) 2851-2860.
30. P. Gahinet, A. Nemirovski, A. Laub, M. Chilali, LMI Control Toolbox User's Guide, The Mathworks, MA, 1995.
31. S. He, F. Liu, Exponential stability for uncertain neutral systems with Markov jumps, Journal of Control Theory and Applications 7(2009) 35-40.
32. A. Bellen, N. Guglielmi, A. E. Ruehli, Methods for linear systems of circuit delay differential equations of neutral type, IEEE Transactions on Circuits and System 46(1999) 212-215.
33. D. Yue, Q. L. Han, A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model, in: Proceedings of the 2004 American Control Conference, IEEE Press, Piscataway, 2004, pp. 5438-5442.
34. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, 1994.