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Exponential stabilization and non-fragile sampled-date dissipative control for uncertain time-varying delay T-S fuzzy systems with state quantization. (English) Zbl 1478.93555

Summary: In this paper, the problem of exponential dissipation stability of T-S fuzzy system with state quantization is studied by using non-fragile sampled-data control. First, A Lyapunov-Krasovskii function containing all sampled-data and quantization information is constructed. Second, the better results can be obtained by using the integral inequality and the Newton Leibniz formula. In addition, a dissipative controller for non-fragile sampled-data is designed. Finally, The reasonable examples illustrate the significant improvement and value of this paper.

MSC:

93D23 Exponential stability
93C57 Sampled-data control/observation systems
93C42 Fuzzy control/observation systems
93C43 Delay control/observation systems
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[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, M.; Qiu, J. B.; Chadli, M., A switched system approach to exponential stabilization of sampled-data T-S fuzzy systems with packet dropouts, IEEE Trans. Cybern., 46, 12, 3145-3156 (2017)
[3] Kim, H. S.; Park, J. B.; Joo, Y. H., A fuzzy Lyapunov-Krasovskii functional approach to sampled-data output-feedback stabilization of polynomial fuzzy systems, IEEE Trans. Fuzzy Syst., 26, 1, 366-373 (2018)
[4] 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)
[5] Wang, L. K.; Lam, H.-K., New stability criterion for continuous-time Takagi-Sugeno fuzzy systems with time-varying delay, IEEE Trans. Circuits, 49, 4, 1551-1556 (2019)
[6] Wang, X. L.; Yang, G. H., Observer-based fault detection for T-S fuzzy systems subject to measurement outliers, Neurocomputing, 335, 21-36 (2019)
[7] Vu, V. P.; Wang, W. J., State/disturbance observer and controller synthesis for the T-S fuzzy system with an enlarged class of disturbances, IEEE Trans. Fuzzy Syst., 26, 6, 3645-3659 (2018)
[8] Makni, S.; Bouattour, M.; Hajjaji, A. E., Robust observer based Fault Tolerant Tracking Control for T-S uncertain systems subject to sensor and actuator faults, ISA Trans., 88, 1-11 (2019)
[9] Su, X. J.; Wen, Y.; Shi, P., Event-triggered fuzzy control for nonlinear systems via sliding mode approach, IEEE Trans. Fuzzy Syst. (2019)
[10] Wang, Y. Y.; Shen, H.; Karimi, H. R., Dissipativity-based fuzzy integral sliding mode control of continuous-time T-S fuzzy systems, IEEE Trans. Fuzzy Syst., 26, 3, 1164-1176 (2018)
[11] Su, X. J.; Xia, F. Q.; Liu, J. X., Event-triggered fuzzy control of nonlinear systems with its application to inverted pendulum systems, Automatica, 94, 236-248 (2018) · Zbl 1401.93129
[12] Zhao, Y.; Wang, J. H.; Yan, F., Adaptive sliding mode fault-tolerant control for type-2 fuzzy systems with distributed delays, Inf. Sci., 473, 227-238 (2019) · Zbl 1448.93048
[13] Gao, Y. B.; Xiao, F.; Liu, J. X., Distributed soft fault detection for interval type-2 fuzzy-model-based stochastic systems with wireless sensor networks, IEEE Trans. Industr. Inf., 15, 1, 334-347 (2019)
[14] Wu, C. W.; Liu, J. X.; Jing, X. J., Adaptive fuzzy control for nonlinear networked control systems, IEEE Trans. Syst. Man Cybern.: Syst., 47, 8, 2420-2430 (2017)
[15] Su, X. J.; Wen, Y.; Shi, P., Event-triggered fuzzy filtering for nonlinear dynamic systems via reduced-order approach, IEEE Trans. Fuzzy Syst., 27, 6, 1215-1225 (2019)
[16] Fridman, E., A refined input delay approach to sampled-data control, Automatica, 46, 2, 421-427 (2010) · Zbl 1205.93099
[17] Wang, Y. Y.; Xia, Y. Q.; Zhou, P. F., Fuzzy-model-based sampled-data control of chaotic systems: a fuzzy time-dependent Lyapunov-Krasovskii functional approach, IEEE Trans. Fuzzy Syst., 25, 6, 1672-1684 (2017)
[18] Tao, R. F.; Ma, Y. C.; Wang, C. J., Stochastic admissibility of singular Markov jump systems with time-delay via sliding mode approach, Appl. Math. Comput., 380, 125-282 (2020)
[19] Yu, P.; Ma, Y. C., Observer-based asynchronous control for Markov jump systems, Appl. Math. Comput., 377, 1225 (2020), 1184
[20] Ge, C.; Shi, Y. P.; Park, J. H., Robust H_∞)stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control, Appl. Math. Comput., 346, 500-512 (2019) · Zbl 1428.93063
[21] Tang, P. Y.; Ma, Y. C., Exponential stabilization and sampled-data H_∞)control for uncertain T-S fuzzy systems with time-varying delay, J. Franklin Inst., 356, 4859-4887 (2019) · Zbl 1414.93149
[22] Wu, H. N.; Wang, Z. P.; Guo, L., \( H_\infty\) sampled-data fuzzy control for attitude tracking of mars entry vehicles with control constraints, Inf. Sci., 475, 182-201 (2019) · Zbl 1448.93076
[23] Shi, K. B.; Wang, J.; Zhong, S. M., New reliable nonuniform sampling control for uncertain chaotic neural networks under Markov switching topologies, Appl. Math. Comput., 347, 169-193 (2019) · Zbl 1428.92015
[24] Han, X. J.; Ma, Y. C., Finite-time extended dissipative control for fuzzy systems with nonlinear perturbations via sampled-data and quantized controller, ISA Trans., 89, 31-44 (2019)
[25] Liang, H. J.; Zhang, Y. H.; Huang, T. W., Prescribed performance cooperative control for multiagent systems with input quantization, IEEE Trans. Cybern., 1-10 (2019)
[26] Tang, X. M.; Deng, L.; Liu, N., Observer-based output feedback MPC for T-S fuzzy system with data loss and bounded disturbance, IEEE Trans. Cybern., 49, 6, 2119-2132 (2019)
[27] Tang, P. Y.; Ma, Y. C., Non-fragile sampled-date dissipative analysis for uncertain T-S fuzzy time delay system with actuator saturation, ISA Trans. (2020)
[28] Shen, H.; Li, F.; Wu, Z. G., Fuzzy-model-based non-fragile control for nonlinear singularly perturbed systems with semi-markov jump parameters, IEEE Trans. Fuzzy Syst., 26, 6, 3428-3439 (2018)
[29] Willems, J. C., Dissipative dynamical systems: I. General theory, Arch. Ration. Mech. Anal., 45, 321-351 (1972) · Zbl 0252.93002
[30] Willems, J. C., Dissipative dynamical systems: II. Linear systems with quadratic supply rates, Arch. Ration. Mech. Anal., 45, 352-393 (1972) · Zbl 0252.93003
[31] Wu, Z. G.; Shi, P.; Su, H. Y., Dissipativity-based sampled-data fuzzy control design and its application to truck-trailer system, IEEE Trans. Fuzzy Syst., 23, 5, 1669-1679 (2015)
[32] Kong, C. F.; Ma, Y. C.; Liu, D. Y., Observer-based quantized sliding mode dissipative control for singular semi-Markovian jump systems, Appl. Math. Comput., 362, 1-18 (2019) · Zbl 1433.93126
[33] Yang, R. N.; Li, L. L.; Su, X. J., Finite-region dissipative dynamic output feedback control for 2-D FM systems with missing measurements, Inf. Sci., 514, 1-14 (2020) · Zbl 1461.93165
[34] Vimal Kumar, S.; Marshal Anthoni, S.; Raja, R., Dissipative analysis for aircraft flight control systems with randomly occurring uncertainties via non-fragile sampled-data control, Math. Comput. Simul., 155, 217-226 (2019) · Zbl 07316553
[35] Yang, R. N.; Li, L. L.; Shi, P., Dissipativity-based two-dimensional control and filtering for a class of switched systems, IEEE Trans. Syst. Man Cybern.: Syst. (2019)
[36] Li, J. Y.; Huang, X. L.; Li, Z. C., Exponential stabilization for fuzzy sampled-data system based on a unified framework and its application, J. Franklin Inst., 354, 5302-5327 (2017) · Zbl 1395.93357
[37] Wang, Y. Y.; Karimi, H. R.; Lam, H.-K., An improved result on exponential stabilization of sampled-data fuzzy systems, IEEE Trans. Fuzzy Syst., 26, 6, 3875-3883 (2018)
[38] Park, P. G.; Lee, W. I.; Lee, S. Y., Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems, J. Franklin Inst., 352, 1378-1396 (2015) · Zbl 1395.93450
[39] Park, M. J.; Kwon, O. M.; Ryu, J. H., Advanced stability criteria for linear systems with time-varying delays, J. Franklin Inst., 355, 520-543 (2018) · Zbl 1380.93189
[40] Liu, F.; Wu, M.; He, Y., New delay-dependent stability criteria for T-S fuzzy systems with time-varying delay, Fuzzy Sets Syst., 161, 1, 2033-2042 (2010) · Zbl 1194.93117
[41] An, J. Y.; Li, T.; Wen, G. L., New stability conditions for uncertain T-S fuzzy systems with interval time-varying delay, Int. J. Control Autom. Syst., 10, 3, 490-497 (2012)
[42] An, J. Y.; Wen, G. L., Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach, Fuzzy Sets Syst., 185, 1, 83-94 (2011) · Zbl 1237.93156
[43] Lian, Z.; He, Y.; Zhang, C. K., Stability analysis for T-S fuzzy systems with time-varying delay via free-matrix-based integral inequality, Int. J. Control Autom. Syst., 14, 1, 21-28 (2016)
[44] An, J. Y.; Liu, X. Z.; Wen, G. L., Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach, J. Nonlinear Sci. Appl., 10, 4, 1941-1959 (2017) · Zbl 1412.37017
[45] Zhu, X. L.; Chen, B.; Yue, D., An improved input delay approach to stabilization of fuzzy systems under variable sampling, IEEE Trans. Fuzzy Syst., 20, 2, 330-341 (2012)
[46] Wu, Z. G.; Shi, P.; Su, H. Y., Sampled-data fuzzy control of chaotic systems based on a T-S fuzzy model, IEEE Trans. Fuzzy Syst., 22, 1, 153-163 (2014)
[47] Liu, Y. J.; Lee, S. M., Stability and stabilization of Takagi-Sugeno fuzzy systems via sampled-data and state quantized controller, IEEE Trans. Fuzzy Syst., 24, 3, 635-644 (2016)
[48] Song, X. N.; Xu, S. Y.; Shen, H., Robust \(H_\infty\) control for uncertain fuzzy systems with distributed delays via output feedback controllers, Inf. Sci., 178, 22, 4341-4356 (2008) · Zbl 1148.93311
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