×

Improved stability analysis of Takagi-Sugeno fuzzy systems with time-varying delays via an extended delay-dependent reciprocally convex inequality. (English) Zbl 07768997

Summary: The problem of stability analysis of Takagi-Sugeno(T-S) fuzzy systems with time-varying delays is investigated in this paper. First, an extended delay-dependent reciprocally convex inequality containing some existing reciprocally convex inequalities is given. Second, a suitable augmented Lyapunov-Krasovskii functional (LKF) is proposed by introducing some new integral vectors \(\int_{t - h_1}^t x(v) dv - x(u)\), \(\int_{t - h_2}^{t - h_1} x(v)dv - x(u)\), and several pairs of \(s\)-dependent integral vectors. Third, the improved stability criteria for T-S fuzzy systems are derived. Finally, several numerical examples are given to illustrate advantages and effectiveness of the proposed criteria by comparing the maximum delay bounds.

MSC:

26-XX Real functions
90-XX Operations research, mathematical programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Luo, J.; Li, M.; Liu, X.; Tian, W.; Zhong, S.; Shi, K., Stabilization analysis for fuzzy systems with a switched sampled-data control, J. Franklin Inst., 357, 1, 39-58 (2020) · Zbl 1451.93214
[2] Shi, K.; Wang, J.; Zhong, S.; Tang, Y.; Cheng, J., Non-fragile memory filtering of TS fuzzy delayed neural networks based on switched fuzzy sampled-data control, Fuzzy Sets Syst., 394, 40-64 (2020) · Zbl 1452.93021
[3] Kavikumar, R.; Sakthivel, R.; Kwon, O.; Kaviarasan, B., Reliable non-fragile memory state feedback controller design for fuzzy markov jump systems, Nonlinear Anal.: Hybrid Syst., 35 (2020), 100828 · Zbl 1433.93039
[4] Feng, Z.; Wei, X. Z., Improved stability condition for Takagi-Sugeno fuzzy systems with time-varying delay, IEEE Trans. Cybern., 47, 3, 1-10 (2016)
[5] Peng, C.; Fei, M. R., An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay, Fuzzy Sets Syst., 212, 97-109 (2013) · Zbl 1285.93054
[6] S. Rathinasamy, K. R, A. Mohammadzadeh, O.M. Kwon, B. Kaviarasan, Fault estimation for mode-dependent IT2 fuzzy systems with quantized output signals, IEEE Trans. Fuzzy Syst. 29(2) (2020) 298-309.
[7] Tian, Y.; Wang, Z., A switched fuzzy filter approach to H_∞)filtering for Takagi-Sugeno fuzzy Markov jump systems with time delay: The continuous-time case, Inf. Sci., 557, 236-249 (2021) · Zbl 1489.93126
[8] Zhao, L.; Gao, H.; Karimi, H. R., Robust stability and stabilization of uncertain T-S fuzzy systems with time-varying delay: an input-output approach, IEEE Trans. Fuzzy Syst., 21, 5, 883-897 (2013)
[9] Zeng, K.; Zhang, N.; Xu, W., A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators, IEEE Trans. Fuzzy Syst., 8, 6, 773-780 (2000)
[10] Kwon, O. M.; Park, M. J.; Park, J. H.; Lee, S. M., Stability and stabilization of T-S fuzzy systems with time-varying delays via augmented Lyapunov-Krasovskii functionals, Inf. Sci., 372, 1-15 (2016) · Zbl 1429.93203
[11] Lian, Z.; He, Y.; Zhang, C.-K.; Wu, M., Stability and stabilization of T-S fuzzy systems with time-varying delays via delay-product-type functional method, IEEE Trans. Cybern., 50, 6, 2580-2589 (2019)
[12] Li, Z.; Yan, H.; Zhang, H.; Sun, J.; Lam, H.-K., Stability and stabilization with additive freedom for delayed Takagi-Sugeno fuzzy systems by intermediary polynomial-based functions, IEEE Trans. Fuzzy Syst., 28, 4, 692-705 (2019)
[13] Zhang, Z.; Chong, L.; Bing, C., New stability and stabilization conditions for T-S fuzzy systems with time delay, Fuzzy Sets Syst., 263, 82-91 (2015) · Zbl 1361.93031
[14] Shi, K.; Wang, J.; Tang, Y.; Zhong, S., Reliable asynchronous sampled-data filtering of T-S fuzzy uncertain delayed neural networks with stochastic switched topologies, Fuzzy Sets Syst., 381, 1-25 (2020) · Zbl 1464.93081
[15] Lian, Z.; He, Y.; Zhang, C. K.; Wu, M., Further robust stability analysis for uncertain Takagi-Sugeno fuzzy systems with time-varying delay via relaxed integral inequality, Inf. Sci., 409, 139-150 (2017) · Zbl 1432.93269
[16] Souza, F. O.; Campos, V. C.S.; Palhares, R. M., On delay-dependent stability conditions for Takagi-Sugeno fuzzy systems, J. Franklin Inst., 351, 7, 3707-3718 (2014) · Zbl 1290.93130
[17] Tan, J.; Dian, S.; Zhao, T.; Chen, L., Stability and stabilization of T-S fuzzy systems with time delay via Wirtinger-based double integral inequality, Neurocomputing, 275, 1063-1071 (2018)
[18] Wang, L.; Liu, J., Local stability analysis for continuous-time Takagi-Sugeno fuzzy systems with time delay, Neurocomputing, 273, 152-158 (2018)
[19] Wang, L.; Lam, H. K., New stability criterion for continuous-time Takagi-Sugeno fuzzy systems with time-varying delay, IEEE Trans. Cybern., 49, 4, 1551-1556 (2018)
[20] Datta, R.; Dey, R.; Bhattacharya, B.; Saravanakumar, R.; Kwon, O.-M., Stability and stabilization of T-S fuzzy systems with variable delays via new Bessel-Legendre polynomial based relaxed integral inequality, Inf. Sci., 522, 99-123 (2020) · Zbl 1461.93412
[21] Zhao, T.; Huang, M.; Dian, S., Stability and stabilization of TS fuzzy systems with two additive time-varying delays, Inf. Sci., 494, 174-192 (2019) · Zbl 1454.93217
[22] Park, M.; Lee, S.; Kwon, O.; Ryu, J., Enhanced stability criteria of neural networks with time-varying delays via a generalized free-weighting matrix integral inequality, J. Franklin Inst., 355, 14, 6531-6548 (2018) · Zbl 1398.93278
[23] Park, M.-J.; Kwon, O.; Ryu, J., Advanced stability criteria for linear systems with time-varying delays, J. Franklin Inst., 355, 1, 520-543 (2018) · Zbl 1380.93189
[24] Zhao, Y.; Gao, H.; Lam, J.; Du, B., Stability and stabilization of delayed T-S fuzzy systems: a delay partitioning approach, IEEE Trans. Fuzzy Syst., 17, 4, 750-762 (2009)
[25] Souza, F. O.; Mozelli, L. A.; Palhares, R. M., On stability and stabilization of T-S fuzzy time-delayed systems, IEEE Trans. Fuzzy Syst., 17, 6, 1450-1455 (2009)
[26] Rhee, B. J.; Won, S., A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design, Fuzzy Sets Syst., 157, 9, 1211-1228 (2006) · Zbl 1090.93025
[27] Wang, L.; Lam, H., A new approach to stability and stabilization analysis for continuous-time Takagi-Sugeno fuzzy systems with time delay, IEEE Trans. Fuzzy Syst., 26, 4, 2460-2465 (2018)
[28] Elias, L. J.; Faria, F. A.; Araujo, R.; Oliveira, V. A., Stability analysis of Takagi-Sugeno systems using a switched fuzzy Lyapunov function, Inf. Sci., 543, 43-57 (2021) · Zbl 1478.93344
[29] Zheng, H.; Xie, W.-B.; Lam, H.-K.; Wang, L., Membership-function-dependent stability analysis and local controller design for T-S fuzzy systems: a space-enveloping approach, Inf. Sci., 548, 233-253 (2021) · Zbl 1478.93356
[30] Liao, X.; Chen, G.; Sanchez, E. N., Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach, Neural Networks, 15, 7, 855-866 (2002)
[31] Gu, K.; Chen, J.; Kharitonov, V. L., Stability of time-delay systems (2003), Springer Science & Business Media · Zbl 1039.34067
[32] Seuret, A.; Gouaisbaut, F., Wirtinger-based integral inequality: application to time-delay systems, Automatica, 49, 9, 2860-2866 (2013) · Zbl 1364.93740
[33] Park, P.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 1, 235-238 (2011) · Zbl 1209.93076
[34] A. Seuret, F. Gouaisbaut, Delay-dependent reciprocally convex combination lemma, Rapport LAAS n16006 (2016) hal-01257670. · Zbl 1447.93265
[35] Zhang, C.-K.; He, Y.; Jiang, L.; Wu, M.; Wang, Q.-G., An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay, Automatica, 85, 481-485 (2017) · Zbl 1375.93094
[36] Zhang, X.-M.; Han, Q.-L.; Seuret, A.; Gouaisbaut, F., An improved reciprocally convex inequality and an augmented Lyapunov-Krasovskii functional for stability of linear systems with time-varying delay, Automatica, 84, 221-226 (2017) · Zbl 1375.93114
[37] Zhang, R.; Zeng, D.; Park, J. H.; Zhong, S.; Liu, Y.; Zhou, X., New approaches to stability analysis for time-varying delay systems, J. Franklin Inst., 356, 7, 4174-4189 (2019) · Zbl 1412.93088
[38] A. Seuret, Gouaisbaut, Allowable delay sets for the stability analysis of linear time-varying delay systems using a delay-dependent reciprocally convex lemma, IFAC-PapersOnLine 50(1) (2017) 1275-1280.
[39] M.C. de Oliveira, R.E. Skelton, Stability tests for constrained linear systems, in: Perspectives in robust control, Springer, 241-257, 2001. · Zbl 0997.93086
[40] Yang, B.; Wang, J.; Liu, X., Improved delay-dependent stability criteria for generalized neural networks with time-varying delays, Inf. Sci., 420, 299-312 (2017) · Zbl 1447.34064
[41] Park, M.; Kwon, O.; Ryu, J., Passivity and stability analysis of neural networks with time-varying delays via extended free-weighting matrices integral inequality, Neural Networks, 106, 67-78 (2018) · Zbl 1443.93098
[42] Yang, B.; Cao, J.; Hao, M.; Pan, X., Further stability analysis of generalized neural networks with time-varying delays based on a novel Lyapunov-Krasovskii functional, IEEE Access, 7, 91253-91264 (2019)
[43] Wang, B.; Yan, J.; Cheng, J.; Zhong, S., New criteria of stability analysis for generalized neural networks subject to time-varying delayed signals, Appl. Math. Comput., 314, 322-333 (2017) · Zbl 1426.93241
[44] Zeng, H. B.; Park, J. H.; Xia, J. W.; Xiao, S. P., Improved delay-dependent stability criteria for T-S fuzzy systems with time-varying delay, Appl. Math. Comput., 235, 492-501 (2014) · Zbl 1334.93110
[45] Huang, L.; Xie, X.; Tan, C., Improved stability criteria for T-S fuzzy systems with time-varying delay via convex analysis approach, Iet Control Theory Appl., 10, 15, 1888-1895 (2016)
[46] Aravindh, D.; Sakthivel, R.; Kong, F.; Anthoni, S. M., Finite-time reliable stabilization of uncertain semi-Markovian jump systems with input saturation, Appl. Math. Comput., 384 (2020), 125388 · Zbl 1508.93235
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.