A generalized probability-interval-decomposition approach for stability analysis of T-S fuzzy systems with stochastic delays. (English) Zbl 1393.93136
Summary: Based on the generalized probability-interval-decomposition approach, the delay-dependent stability analysis for a class of T-S fuzzy systems with stochastic delays is investigated. The information of the probability distribution of stochastic delay is fully exploited and a series of sufficient stability criteria are obtained. A rigorous mathematical proof is provided that the conservatism of the proposed stability criteria can be reduced progressively by increasing the number of the probability interval. Based on this, a novel hierarchy of LMI conditions is established. It is rigorously proved that with the same decomposition of probability interval, the conservatism of the proposed stability criteria is less than the one obtained by time-varying delay decomposition approach. The computation burden of the proposed method is analyzed and compared with one of the time-varying delay decomposition approach. Finally, a numerical example is given to illustrate the validness and effectiveness of the proposed approach.
Keywords:
probability-interval-decomposition approach; stability analysis; T-S fuzzy systems; stochastic delaysReferences:
| [1] | Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE Trans. Syst. Man Cybern., 15, 1, 116-132, (1985) · Zbl 0576.93021 |
| [2] | Lien, C.; Yu, K.; Chen, W.; Wan, Z.; Chung, Y., Stability criteria for uncertain Takagi-sugeno fuzzy systems with interval time-varying delay, IET Control Theory Appl., 1, 3, 764-769, (2007) |
| [3] | Jiang, X.; Han, Q. L., Robust H∞ control for uncertain Takagi-sugeno fuzzy systems with interval time-varying delay, IEEE Trans. Fuzzy Syst., 15, 2, 321-331, (2007) |
| [4] | Yang, F.; Guan, S.; Wang, D., Quadratically convex combination approach to stability of T-S fuzzy systems with time-varying delay, J. Franklin Inst., 351, 7, 3752-3765, (2014) · Zbl 1290.93114 |
| [5] | Tian, E.; Peng, C., Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay, Fuzzy Sets Syst., 157, 4, 544-559, (2006) · Zbl 1082.93031 |
| [6] | Li, L.; Liu, X.; Chai, T., New approaches on H∞ control of T-S fuzzy systems with interval time-varying delay, Fuzzy Sets Syst., 160, 12, 1669-1688, (2009) · Zbl 1175.93127 |
| [7] | Kwon, O. M.; Park, M. J.; Lee, S. M.; Ju, H. P., Augmented Lyapunov-krasovskii functional approaches to robust stability criteria for uncertain Takagi-sugeno fuzzy systems with time-varying delays, Fuzzy Sets Syst., 201, 16, 1-19, (2012) · Zbl 1251.93072 |
| [8] | Peng, C.; Wen, L.; Yang, J., On delay-dependent robust stability criteria for uncertain T-S fuzzy systems with interval time-varying delay, Int. J. Fuzzy Syst., 13, 1, 35-44, (2011) |
| [9] | Huang, L.; Xie, X. H.; 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) |
| [10] | Zhang, X.; Han, Q. L., A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays, Int. J. Robust Nonlinear, 19, 17, 1922-1930, (2009) · Zbl 1185.93106 |
| [11] | Yue, D.; Tian, E.; Zhang, Y., A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay, Int. J. Robust Nonlinear, 19, 13, 1493-1518, (2009) · Zbl 1298.93259 |
| [12] | Peng, C.; Yue, D.; Tian, Y. C., New approach on robust delay-dependent H∞ control for uncertain T-S fuzzy systems with interval time-varying delay, IEEE Trans. Fuzzy Syst., 17, 4, 890-900, (2009) |
| [13] | Tian, E.; Yue, D.; Gu, Z., Robust H∞ control for nonlinear system over network: a piecewise analysis method, Fuzzy Sets Syst., 161, 21, 2731-2745, (2010) · Zbl 1206.93037 |
| [14] | An, J.; Wen, G., 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 |
| [15] | 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, 1, 97-109, (2013) · Zbl 1285.93054 |
| [16] | Yang, J.; Luo, W. P.; Cheng, J.; Wang, Y. H., Further improved stability criteria for uncertain T-S fuzzy systems with interval time-varying delay by delay-partitioning approach, ISA Trans., 58, 27-34, (2015) |
| [17] | Yang, J.; Luo, W. P.; Wang, Y. H.; Cheng, J., Further improved stability criteria for uncertain T-S fuzzy systems with time-varying delay by (m,N)-delay-partitioning approach, ISA Trans., 59, 20-28, (2015) |
| [18] | Bao, H.; Cao, J., Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay, Neural Networks, 24, 1, 19-28, (2011) · Zbl 1222.93213 |
| [19] | Zhang, G.; Wang, T.; Li, T.; Fei, S., Delay-derivative-dependent stability criterion for neural networks with probabilistic time-varying delay, Int. J. Syst. Sci., 44, 11, 2140-2151, (2013) · Zbl 1307.93447 |
| [20] | Johan, N., Real-time control systems with delays, (1998), Department of Automatic Control, Lund Institute of Technology Sweden, Lund |
| [21] | Peng, C.; Han, Q. L.; Yue, D., Communication-delay-distribution dependent decentralized control for large-scale systems with IP-based communication networks, IEEE Trans. Control Syst. Technol., 21, 3, 820-830, (2013) |
| [22] | Peng, C.; Zhang, J., Delay-distributed-dependent load frequency control of power systems with probabilistic interval delays, IEEE Trans. Power Syst., 31, 4, 3309-3317, (2016) |
| [23] | Lu, C.; Zhang, X.; Wang, X.; Han, Y., Mathematical expectation modeling of wide-area controlled power systems with stochastic time delay, IEEE Trans. Smart Grid, 6, 3, 1511-1519, (2015) |
| [24] | Zhang, F.; Sun, Y.; Cheng, L.; Li, X.; Chow, J. H.; Zhao, W., Measurement and modeling of delays in wide-area closed-loop control systems, IEEE Trans. Power Syst., 30, 5, 2426-2433, (2015) |
| [25] | Wen, S.; Yu, X.; Zeng, Z.; Wang, J., Event-triggering load frequency control for multiarea power systems with communication delays, IEEE Trans. Ind. Electron., 63, 2, 1308-1317, (2016) |
| [26] | Wang, S.; Meng, X.; Chen, T., Wide-area control of power system through delayed network communication, IEEE Trans. Control Syst. Technol., 20, 2, 495-503, (2012) |
| [27] | Jiang, L.; Yao, W.; Wu, Q.; Wen, J.; Cheng, S., Delay-dependent stability for load frequency control with constant and time-varying delays, IEEE Trans. Power Syst., 27, 2, 932-941, (2012) |
| [28] | Zhang, C. K.; Jiang, L.; Wu, Q.; He, Y.; Wu, M., Further results on delay-dependent stability of multi-area load frequency control, IEEE Trans. Power Syst., 28, 4, 4465-4474, (2013) |
| [29] | Zhang, C. K.; Jiang, L.; Wu, Q.; He, Y.; Wu, M., Delay-dependent robust load frequency control for time delay power systems, IEEE Trans. Power Syst., 28, 3, 2192-2201, (2013) |
| [30] | Zhang, Z.; Lin, C.; Chen, B., New stability and stabilization conditions for T-S fuzzy systems with time delay, Fuzzy Set Syst., 263, 15, 82-91, (2015) · Zbl 1361.93031 |
| [31] | Qiu, J.; Karimi, H. R., Fuzzy-affine-model-based memory filter design of nonlinear systems with time-varying delay, IEEE Trans. Fuzzy Syst., 99, (2017) |
| [32] | Feng, Z.; Zheng, W. X., Improved stability condition for Takagi-sugeno fuzzy systems with time-varying delay, IEEE Trans. Cybern., 47, 3, 661-670, (2017) |
| [33] | 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 functional, Inform. Sciences, 372, 1-15, (2016) · Zbl 1429.93203 |
| [34] | Wei, Y.; Qiu, J.; Karimi, H. R.; Wang, M., New results on H∞ dynamic output feedback control for Markovian jump systems with time-varying delay and defective mode information, Optim. Control Appl. Methods, 35, 6, 656-675, (2014) · Zbl 1305.93184 |
| [35] | Wei, Y.; Qiu, J.; Fu, S., Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay, Nonlinear Anal. Hybrid Syst., 16, 52-71, (2015) · Zbl 1310.93075 |
| [36] | Wei, Y.; Qiu, J.; Karimi, H. R., Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults, IEEE Trans. Circuits Syst. I Regul. Papers, 64, 1, 170-181, (2017) |
| [37] | Li, L.; Ding, S. X.; Qiu, J.; Yang, Y.; Zhang, Y., Weighted fuzzy observer-based fault detection approach for discrete-time nonlinear systems via piecewise-fuzzy Lyapunov functions, IEEE Trans. Fuzzy Syst., 24, 6, 1320-1333, (2016) |
| [38] | Li, L.; Ding, S. X.; Qiu, J.; Yang, Y., Real-time fault detection approach for nonlinear systems and its asynchronous T-S fuzzy observer-based implementation, IEEE Trans. Cybern., 47, 2, 283-294, (2017) |
| [39] | Wang, T.; Zhang, Y.; Qiu, J.; Gao, H., Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements, IEEE Trans. Fuzzy Syst., 23, 2, 302-312, (2015) |
| [40] | Wang, T.; Qiu, J.; Gao, H.; Wang, C., Network-based fuzzy control for nonlinear industrial processes with predictive compensation strategy, IEEE Trans. Syst. Man Cybern. Syst., 47, 8, 2137-2147, (2016) |
| [41] | Qiu, J.; Ding, S. X.; Gao, H.; Yin, S., Fuzzy-model-based reliable static output feedback H∞ control of nonlinear hyperbolic PDE systems, IEEE Trans. Fuzzy Syst., 24, 2, 388-400, (2016) |
| [42] | Wang, T.; Qiu, J.; Fu, S.; Ji, W., Distributed fuzzy H∞ filtering for nonlinear multirate networked double-layer industrial processes, IEEE Trans. Ind. Electron., 64, 6, 5203-5211, (2017) |
| [43] | Wang, T.; Gao, H.; Qiu, J., A combined fault-tolerant and predictive control for network-based industrial processes, IEEE Trans. Ind. Electron., 63, 4, 2529-2536, (2016) |
| [44] | Wang, T.; Gao, H.; Qiu, J., A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control, IEEE Trans. Neural Networks Learn. Syst., 27, 2, 416-425, (2016) |
| [45] | Peng, C.; Yue, D.; Tian, E.; Gu, Z., A delay distribution based stability analysis and synthesis approach for networked control systems, J. Franklin Inst., 346, 4, 349-365, (2009) · Zbl 1166.93381 |
| [46] | Yue, D.; Tian, E.; Zhang, Y.; Peng, C., Delay-distribution-dependent robust stability of uncertain systems with time-varying delay, Int. J. Robust Nonlinear, 19, 4, 377-393, (2009) · Zbl 1157.93478 |
| [47] | Yue, D.; Tian, E.; Zhang, Y.; Peng, C., Delay-distribution-dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay, IEEE Trans. Syst. Man Cybern. B, 39, 2, 503-536, (2009) |
| [48] | Peng, C.; Yang, T., Communication-delay-distribution-dependent networked control for a class of T-S fuzzy systems, IEEE Trans. Fuzzy Syst., 18, 2, 326-335, (2010) |
| [49] | Lakshmanan, S.; Park, J. H.; Lee, T. H.; Jung, H. Y.; Rakkiyappan, R., Stability criteria for BAM neural networks with leakage delays and probabilistic time-varying delays, Appl. Math. Comput., 219, 17, 9408-9423, (2013) · Zbl 1294.34075 |
| [50] | Muthukumar, P.; Subramaniana, K.; Lakshmanan, S., Robust finite time stabilization analysis for uncertain neural networks with leakage delay and probabilistic time-varying delays, J. Franklin Inst., 353, 16, 4091-4113, (2016) · Zbl 1347.93222 |
| [51] | Li, R.; Cao, J.; Tu, Z., Passivity analysis of memristive neural networks with probabilistic time-varying delays, Neurocomputing, 191, 249-262, (2016) |
| [52] | Ma, C.; Shi, P.; Zhao, X.; Zeng, Q., Consensus of Euler-Lagrange systems networked by sampled-data information with probabilistic time delays, IEEE Trans. Cybern., 45, 6, 1126-1133, (2015) |
| [53] | Gu, K.; Kharitonov, V. L.; Chen, J., Stability of time-delay systems, (2003), Birkhauser Boston, MA · Zbl 1039.34067 |
| [54] | Peet, M; Papachristodoulou, A., Positive forms and stability of linear time-delay systems, SIAM J. Control Optim., 47, 6, 3237-3258, (2009) · Zbl 1187.34101 |
| [55] | Seuret, A.; Gouaisbaut, F., Hierarchy of LMI conditions for the stability analysis of time-delay systems, Syst. Control Lett., 81, 1, 1-7, (2015) · Zbl 1330.93211 |
| [56] | Horn, R. A., Matrix analysis, (2013), Cambridge University Press New York, USA · Zbl 1267.15001 |
| [57] | Horn, R. A., Topics in matrix analysis, (1991), Cambridge University Press New York, USA · Zbl 0729.15001 |
| [58] | Park, P.; Ko, J.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 1, 235-238, (2011) · Zbl 1209.93076 |
| [59] | Ren, W.; Cao, Y., Distributed coordination of multi-agent networks, (2011), Springer London · Zbl 1225.93003 |
| [60] | Seuret, A.; Gouaisbaut, F., Wirtinger-based integral inequality: application to time-delay systems, Automatica, 49, 9, 2860-2866, (2013) · Zbl 1364.93740 |
| [61] | Kim, J., Further improvement of Jensen inequality and application to stability of time-delayed systems, Automatica, 64, 1, 121-125, (2016) · Zbl 1329.93123 |
| [62] | Zeng, H.; He, Y.; Wu, M.; She, J., Free-matrix-based integral inequality for stability analysis of systems with time-varying delay, IEEE Trans. Autom. Control, 60, 10, 2768-2772, (2015) · Zbl 1360.34149 |
| [63] | Wu, M.; He, Y.; She, J., Stability analysis and robust control of time-delay systems, (2010), Science Press, Springer-Verlag Beijing · Zbl 1250.93005 |
| [64] | Liu, J.; Zhang, J., Note on stability of discrete-time time-varying delay systems, IET Control Theory Appl., 6, 2, 335-337, (2012) |
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.
