Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India
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.
 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.  S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear matrix inequalities in system and control theory, Soc. Ind. Appl. Math., Philadelphia, 1994.
 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.  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.  L. Dai, Singular Control Systems, Springer-Verlag : Berlin, 1989.  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.  M. Fang, Delay-dependent stabililty analysis for discrete singular systems with time-varying delays, Acta Automat. Sinica, 36(5) (2010), 751-755.  Z. Feng and J. Lam, Robust reliable dissipative ltering for discrete delay singular systems, Signal Process., 92(12) (2012), 3010-3025.  C. Huang, Stability analysis of discrete singular fuzzy systems, Fuzzy Sets Syst., 151(1) (2005), 155-165.  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.  F. L. Lewis, A survey of linear singular systems, Circuits Syst. Signal Process., 5(1) (1986), 3-36.  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.  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.  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.  I. R. Petersen, A stabilization algorithm for a class of uncertain linear systems, Systems Control Lett., 8(4) (1987), 351-357.  H. Rotstein, M. Sznaier and M. Idan, H2=H1 ltering theory and an aerospace application, Int. J. Robust Nonlinear Control, 6 (1996), 347-366.  T. Takagi and M. Sugeno, Fuzzy identication of systems and its applications to modelling and control, IEEE Trans. Syst. Man Cybern., 15(1) (1985), 116-132.  K. Tanaka and M. Sugeno, Stability analysis and design of fuzzy control systems, Fuzzy Sets Syst., 45(2) (1992), 135-156.  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.  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.  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.  Z. Wu, P. Shi, H. Su and J. Chu, Reliable H1 control for discrete-time fuzzy systems with innite-distributed delay, IEEE Trans. Fuzzy Syst., 20(1) (2012), 22-31.  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.  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.  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.  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.
 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.  Q. L. Zhang, Decentralized control and robust control for singular systems, Xian : North- western University Press, 1997.  J. Zhang and Y. Zhao, Asymptotic stability of nonlinear singular discrete systems, Proc. IEEE Int. Conf. Multimedia Tech., (2011), 2411-2413.  S. Zhao, Quadratic stabilization for a class of switched Nonlinear singular systems, Int. J. Inf. Syst. Sci., 5(3-4) (2009), 425-429.