Membership-difference-dependent switching control for time-delay T-S fuzzy systems. (English) Zbl 1533.93332
Summary: The switching control issue in time-delay Takagi-Sugeno fuzzy systems (TSFS) based on membership difference (MD) is investigated in this paper. For the asymmetric Lyapunov-Krasovskii functional (LKF) selected in this paper, the zero equation based on MD is introduced in the analysis process, and combined with inequality lemmas, the stability conditions of linear matrix inequality (LMI) form are derived. According to the characteristics of MD, the corresponding switching controller is designed and a more concise controller form is given. Compared with the existing literature, the stability condition presented in this paper is less conservative. Finally, two examples are provided to demonstrate the efficacy and superiority of the suggested method.
MSC:
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C42 | Fuzzy control/observation systems |
| 93C43 | Delay control/observation systems |
References:
| [1] | Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cybern., 15, 1, 116-132, 1985 · Zbl 0576.93021 |
| [2] | Wang, X.; Park, J. H.; She, K.; Zhong, S. M.; Shi, L., Stabilization of chaotic systems with T-S fuzzy model and nonuniform sampling: a switched fuzzy control approach, IEEE Trans. Fuzzy Syst., 27, 6, 1263-1271, 2019 |
| [3] | Yang, B. J.; Huang, H.; Cao, L., Centered error entropy-based sigma-point Kalman filter for spacecraft state estimation with non-Gaussian noise, Space: Sci. Technol., 2022 |
| [4] | Cao, L.; Xiao, B.; Golestani, M.; Ran, D., Faster fixed-time control of flexible spacecraft attitude stabilization, IEEE Trans. Ind. Inform., 16, 2, 1281-1290, 2019 |
| [5] | Xiao, B.; Wu, X.; Cao, L.; Hu, X., Prescribed time attitude tracking control of spacecraft with arbitrary disturbance, IEEE Trans. Aerosp. Electron. Syst., 58, 3, 2531-2540, 2022 |
| [6] | Hua, C. C.; Wu, S. S.; Guan, X. P., Stabilization of T-S fuzzy system with time delay under sampled-data control using a new looped-functional, IEEE Trans. Fuzzy Syst., 28, 2, 400-407, 2020 |
| [7] | Peng, C.; Fei, M. R., An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay, Fuzzy Sets and Systems, 212, 97-109, 2013 · Zbl 1285.93054 |
| [8] | Zhao, Y.; Gao, H.; Lam, J.; Du, B. Z., Stability and stabilization of delayed T-S fuzzy systems: A delay partitioning approach, IEEE Trans. Fuzzy Syst., 17, 4, 750-762, 2009 |
| [9] | Zhao, T.; Dian, S. Y., Delay-dependent stabilization of discrete-time interval type-2 T-S fuzzy systems with time-varying delay, J. Franklin Inst. B, 354, 1542-1567, 2017 · Zbl 1355.93153 |
| [10] | Zhang, Z. Y.; Lin, C.; Chen, B., New stability and stabilization conditions for T-S fuzzy systems with time delay, Fuzzy Sets and Systems, 263, 82-91, 2015 · Zbl 1361.93031 |
| [11] | Liu, Y.; Wang, Y. Q., Actuator and sensor fault estimation for discrete-time switched T-S fuzzy systems with time delay, J. Franklin Inst. B, 358, 1619-1634, 2021 · Zbl 1458.93157 |
| [12] | 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, Inform. Sci., 372, 1-15, 2016 · Zbl 1429.93203 |
| [13] | Feng, Z. G.; Wei, X. Z., Improved stability condition for Takagi-Sugeno fuzzy systems with time-varying delay, IEEE Trans. Cybern., 47, 3, 661-670, 2017 |
| [14] | Liu, Y. J.; Park, J. H.; Guo, B. Z.; Shu, Y. J., Further results on stabilization of chaotic systems based on fuzzy memory sampled-data control, IEEE Trans. Fuzzy Syst., 26, 2, 1040-1045, 2018 |
| [15] | Zhang, R. M.; Zeng, D. Q.; Park, J. H.; Liu, Y. J.; Zhong, S. M., A new approach to stabilization of chaotic systems with nonfragile fuzzy proportional retarded sampled-data control, IEEE Trans. Cybern., 49, 9, 1672-1684, 2019 |
| [16] | Wu, M.; He, Y.; She, J. H.; Liu, G. P., Delay-dependent criteria for robust stability of time-varying delay systems, Automatica, 40, 8, 1435-1439, 2004 · Zbl 1059.93108 |
| [17] | Han, Q. L., A discrete delay decomposition approach to stability of linear retarded and neutral systems, Automatica, 45, 2, 517-524, 2009 · Zbl 1158.93385 |
| [18] | 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 |
| [19] | Zeng, H. B.; He, Y.; Wu, M.; She, J., Free-matrix-based integral inequality for stability analysis of systems with time-varying delay, IEEE Trans. Automat. Control, 60, 10, 2768-2772, 2015 · Zbl 1360.34149 |
| [20] | Seuret, A.; Gouaisbaut, F., Stability of linear systems with time-varying delays using bessel Legendre inequalities, IEEE Trans. Automat. Control, 63, 1, 225-232, 2018 · Zbl 1390.34213 |
| [21] | Xu, S. Y.; Lam, J.; Zhang, B. Y.; Zou, Y., New insight into delay-dependent stability of time-delay systems, Internat. J. Robust Nonlinear Control, 25, 961-970, 2015 · Zbl 1312.93077 |
| [22] | Wang, L. K.; Lam, H. K., 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 |
| [23] | Wang, L. K.; Lam, H. K.; Gu, J. H., Stability and stabilization for fuzzy systems with time delay by applying polynomial membership function and iteration algorithm, IEEE Trans. Cybern., 52, 11, 11604-11613, 2022 |
| [24] | Zhang, J.; Wanga, X. H.; Wang, Y. Q., Membership-function-dependent dynamic output feedback \(H_\infty\) controller design of continuous-time T-S fuzzy systems via non-quadratic Lyapunov function, ISA Trans., 134, 212-225, 2023 |
| [25] | Tian, S. N.; Liu, K. Z.; Zhang, M. L.; Lu, C. D.; Chen, L. F.; Wu, M.; She, J. H., Disturbance rejection of T-S fuzzy systems: a membership function-dependent EID method, Internat. J. Systems Sci., 54, 3, 618-632, 2023 · Zbl 1520.93288 |
| [26] | Xu, M. C.; Gu, J.; Xu, Z., Observer-based switching control for T-S fuzzy systems with mixed time delays, Int. J. Fuzzy Syst., 2023 |
| [27] | Qiu, Y. F.; Park, J. H.; Hua, C. C.; Wang, X. J., Stability analysis of time-varying delay T-S fuzzy systems via quadratic-delay-product method, IEEE Trans. Fuzzy Syst., 31, 1, 129-137, 2023 |
| [28] | Seuret, A.; Gouaisbaut, F., Wirtinger-based integral inequality: Application to time-delay systems, Automatica, 49, 9, 2860-2866, 2013 · Zbl 1364.93740 |
| [29] | Z. Sheng, C. Lin, B. Chen, Q. Wang, Stability and stabilization of t-s fuzzy time-delay systems under sampled-data control via new asymmetric functional method, IEEE Trans. Fuzzy Syst. http://dx.doi.org/10.1109/TFUZZ.2023.3247030. |
| [30] | Sheng, Z.; Lin, C.; Chen, B.; Wang, Q., An asymmetric Lyapunov-Krasovskii functional method on stability and stabilization for T-S fuzzy systems with time delay, IEEE Trans. Fuzzy Syst., 30, 6, 2135-2140, 2022 |
| [31] | Wang, L. K.; Lam, H. K., Local stabilization for continuous-time Takagi-Sugeno fuzzy systems with time delay, IEEE Trans. Fuzzy Syst., 26, 1, 379-385, 2018 |
| [32] | Luo, J.; Liu, X.; Tian, W.; Zhong, S.; Shi, K.; Li, M., Finite-time \(H_\infty\) reliable control for T-S fuzzy systems with variable sampling, Physica A, 538, Article 122697 pp., 2020 · Zbl 07571862 |
| [33] | Cheng, J.; Park, J.; Wang, H., Event-triggered \(H_\infty\) control for T-S fuzzy nonlinear systems and its application to truck-trailer system, ISA Trans., 65, 62-71, 2016 |
| [34] | Zhao, Y.; Wang, J. H.; Yan, F.; Shen, Y., Adaptive sliding mode fault-tolerant control for type-2 fuzzy systems with distributed delays, Inform. Sci., 473, 227-238, 2019 · Zbl 1448.93048 |
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