Admissibility analysis for discrete-time singular systems with time-varying delays by adopting the state-space Takagi-Sugeno fuzzy model

Document Type: Research Paper

Authors

Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India

Abstract

This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the lower and upper delay bounds. Finally, numerical examples are provided to substantiate the theoretical results.

Keywords


[1] J. An and G. Wen, Improved stability criteria for time-varying delayed T-S fuzzy systems
via delay partitioning approach, Fuzzy Sets Syst., 185(1) (2011), 83-94.
[2] S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear matrix inequalities in system
and control theory, Soc. Ind. Appl. Math., Philadelphia, 1994.

[3] I. M. Buzurovic and D. LJ. Debeljkovic, Contact problem and controllability for singular
systems in biomedical robotics, Int. J. Inf. Syst. Sci., 6(2) (2010), 128-141.
[4] S. H. Chen and J. H. Chou, Stability robustness of linear discrete singular time-delay systems
with structured parameter uncertainties, IEE Proc. Control Theory Appl., 150(3) (2003),
295-302.
[5] L. Dai, Singular Control Systems, Springer-Verlag : Berlin, 1989.
[6] Y. Ding, S. Zhong and W. Chen, A delay-range-dependent uniformly asymptotic stability
criterion for a class of nonlinear singular systems, Nonlinear Anal. B: Real World Appl.,
12(2) (2011), 1152-1162.
[7] M. Fang, Delay-dependent stabililty analysis for discrete singular systems with time-varying
delays, Acta Automat. Sinica, 36(5) (2010), 751-755.
[8] Z. Feng and J. Lam, Robust reliable dissipative ltering for discrete delay singular systems,
Signal Process., 92(12) (2012), 3010-3025.
[9] C. Huang, Stability analysis of discrete singular fuzzy systems, Fuzzy Sets Syst., 151(1)
(2005), 155-165.
[10] J. Jiao, Robust stability and stabilization of discrete singular systems with interval time-
varying delay and linear fractional uncertainty, Int. J. Autom. Comput., 9(1) (2012), 8-15.
[11] F. L. Lewis, A survey of linear singular systems, Circuits Syst. Signal Process., 5(1) (1986),
3-36.
[12] J. Li, H. Su, Z. Wu and J. Chu, Robust stabilization for discrete-time nonlinear Singular
systems with mixed time delays, Asian J. Control, 14(1) (2012), 1411-1421.
[13] J. Li, H. Su, Z. Wu and J. Chu, Less conservative robust stability criteria for uncertain
discrete stochastic singular systems with time-varying delay, Int. J. Syst. Sci., 44(3) (2013),
432-441.
[14] J. Lin, S. Fei and J. Shen, Delay-dependent H1 ltering for discrete-time singular Markovian
jump systems with time-varying delay and partially unknown transition probabilities, Signal
Process., 91(2) (2011), 277-289.
[15] I. R. Petersen, A stabilization algorithm for a class of uncertain linear systems, Systems
Control Lett., 8(4) (1987), 351-357.
[16] H. Rotstein, M. Sznaier and M. Idan, H2=H1 ltering theory and an aerospace application,
Int. J. Robust Nonlinear Control, 6 (1996), 347-366.
[17] T. Takagi and M. Sugeno, Fuzzy identi cation of systems and its applications to modelling
and control, IEEE Trans. Syst. Man Cybern., 15(1) (1985), 116-132.
[18] K. Tanaka and M. Sugeno, Stability analysis and design of fuzzy control systems, Fuzzy Sets
Syst., 45(2) (1992), 135-156.
[19] T. Taniguchi, K. Tanaka and H. O. Wang, Fuzzy descriptor systems and nonlinear model
following control, IEEE Trans. Fuzzy Syst., 8(4) (2000), 265-452.
[20] Y. Wang, Z. Sun and F. Sun, Robust fuzzy control of a class of nonlinear descriptor systems
with time-varying delay, Int. J. Control Autom. Syst., 2(1) (2004), 76-82.
[21] Z.Wu, J. H. Park, H. Su and J. Chu, Admissibility and dissipativity analysis for discrete-time
singular systems with mixed time-varying delays, Appl. Math. Comput., 218(13) (2012),
7128-7138.
[22] Z. Wu, P. Shi, H. Su and J. Chu, Reliable H1 control for discrete-time fuzzy systems with
in nite-distributed delay, IEEE Trans. Fuzzy Syst., 20(1) (2012), 22-31.
[23] Z. Wu, H. Su and J. Chu, Robust exponential stability of uncertain singular markovian jump
time-delay systems, Acta Automat. Sinica, 36(4) (2010), 558-563.
[24] Y. Xia, L. Li, M. S. Mahmoud and H. Yang, H1 ltering for nonlinear singular markovian
jumping systems with interval time-varying delays, Int. J. Syst. Sci., 43(2) (2012), 272-284.
[25] H. Xin, D. Gan, M. Huang and K. Wang, Estimating the stability region of singular perturba-
tion power systems with saturation nonlinearities: an linear matrix inequality-based method,
IET Control Theory Appl., 4(3) (2010), 351-361.
[26] 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. Autom. Control, 47(7)
(2002), 1122-1128.

[27] S. Xu, B. Song, J. Lu and J. Lam, Robust stability of uncertain discrete-time singular fuzzy
systems, Fuzzy Sets Syst., 158(20) (2007), 2306-2316.
[28] Q. L. Zhang, Decentralized control and robust control for singular systems, Xian : North-
western University Press, 1997.
[29] J. Zhang and Y. Zhao, Asymptotic stability of nonlinear singular discrete systems, Proc.
IEEE Int. Conf. Multimedia Tech., (2011), 2411-2413.
[30] S. Zhao, Quadratic stabilization for a class of switched Nonlinear singular systems, Int. J.
Inf. Syst. Sci., 5(3-4) (2009), 425-429.