Extended dissipativity analysis of singular Takagi-Sugeno fuzzy systems with time delay via two improved techniques. (English) Zbl 1485.93320
This paper is devoted to investigation of the extended dissipativity analysis for singular Takagi-Sugeno fuzzy system with time delay. The results of the paper related to some estimates of Lyapunov-Krasovskii functional generalize those reported in [H.-B. Zeng et al., Automatica 60, 189–192 (2015; Zbl 1331.93166); J. Sun et al., Automatica 46, No. 2, 466–470 (2010; Zbl 1205.93139); W. Li et al., “Admissibility analysis for Takagi-Sugeno fuzzy singular systems with time delay”, Neurocomputing, 205, 336–340 (2016;doi:10.1016/j.neucom.2016.04.035); H. Huang et al., “Further result on guaranteed \(H^{\infty}\) performance state estimation of delayed static neural networks”, IEEE Trans. Neural Networks Learning Syst. 26, No. 6, 1335–1341 (2015; doi:10.1109/TNNLS.2014.2334511)].
A novel sufficient criterion with less conservativeness or less computational demand is derived to ensure the investigated system to be admissible and extended dissipative. Some numerical example showing the effectiveness of the obtained results is presented.
It is worth to add that in modern control theory dissipativity analysis of control systems considers system description and stability analysis from the perspective of energy input and output.
A novel sufficient criterion with less conservativeness or less computational demand is derived to ensure the investigated system to be admissible and extended dissipative. Some numerical example showing the effectiveness of the obtained results is presented.
It is worth to add that in modern control theory dissipativity analysis of control systems considers system description and stability analysis from the perspective of energy input and output.
Reviewer: Wiesław Kotarski (Sosnowiec)
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93C43 | Delay control/observation systems |
| 93C10 | Nonlinear systems in control theory |
| 93B35 | Sensitivity (robustness) |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
Keywords:
extended dissipativity; singular system; Takagi-Sugeno fuzzy system; integral inequality; time delayReferences:
| [1] | Aslam, M.; Zhang, B.; Zhang, Y.; Zhang, Z., Extended dissipative filter design for T-S fuzzy systems with multiple time delays, ISA Transactions, 80, 22-34 (2018) · doi:10.1016/j.isatra.2018.05.014 |
| [2] | Chen, J.; Park, J.; Xu, S., Stability analysis for neural networks with time-varying delay via improved techniques, IEEE Transactions on Cybernetics, 49, 12, 4495-4500 (2019) · doi:10.1109/TCYB.6221036 |
| [3] | Gao, T.; Liu, Y.; Liu, L.; Li, D., Adaptive neural network-based control for a class of nonlinear pure-feedback systems with time-varying full state constraints, IEEE/CAA Journal of Automatica Sinica, 5, 5, 923-933 (2018) · doi:10.1109/JAS.2018.7511195 |
| [4] | Han, C.; Wu, L.; Shi, P.; Zeng, Q., On dissipativity of Takagi-Sugeno fuzzy descriptor systems with time-delay, Journal of the Franklin Institute, 349, 10, 3170-3184 (2015) · Zbl 1259.93075 · doi:10.1016/j.jfranklin.2012.10.007 |
| [5] | Han, C.; Zeng, Y.; Zhang, H.; Zhao, Y., Admissibility analysis for nonlinear singular system with time delay via T-S fuzzy model, International Journal of Fuzzy Systems, 19, 1, 207-214 (2017) · doi:10.1007/s40815-015-0138-9 |
| [6] | Hua, C.; Wu, S.; Guan, X., Stabilization of T-S fuzzy system with time delay under sampled-data control using a new looped-functional, IEEE Transactions on Fuzzy Systems, 28, 400-407 (2020) · doi:10.1109/TFUZZ.2019.2906040 |
| [7] | Huang, H.; Huang, T.; Cao, Y., Reduced-order filtering of delayed static neural networks with Markovian jumping parameters, IEEE Transactions on Neural Networks and Learning Systems, 29, 11, 5606-5618 (2018) · doi:10.1109/TNNLS.2018.2806356 |
| [8] | Huang, H.; Huang, T.; Chen, X., Further result on guaranteed \(####\) performance state estimation of delayed static neural networks, IEEE Transactions on Neural Networks and Learning Systems, 26, 6, 1335-1341 (2015) · doi:10.1109/TNNLS.2014.2334511 |
| [9] | Li, J.; Huang, X.; Li, Z., Extended dissipative filtering of fuzzy systems with time-varying delay under imperfect premise matching, International Journal of Fuzzy Systems, 48, 1731-1743 (2017) · Zbl 1362.93088 · doi:10.1080/00207721.2017.1282058 |
| [10] | Li, W.; Feng, Z.; Sun, W.; Zhang, J., Admissibility analysis for Takagi-Sugeno fuzzy singular systems with time delay, Neurocomputing, 205, 12, 336-340 (2016) · doi:10.1016/j.neucom.2016.04.035 |
| [11] | Liu, L.; Liu, Y.; Li, D.; Tong, S.; Wang, Z., Barrier Lyapunov function based adaptive fuzzy FTC for switched systems and its applications to resistance inductance capacitance circuit system, IEEE Transactions on Cybernetics (2020) · doi:10.1109/TCYB.2019.2931770 |
| [12] | Liu, L.; Liu, Y.; Tong, S., Fuzzy based multierror constraint control for switched nonlinear systems and its applications, IEEE Transactions on Fuzzy Systems, 27, 8, 1519-1531 (2019) · doi:10.1109/TFUZZ.2018.2882173 |
| [13] | Liu, L.; Liu, Y.; Tong, S.; Chen, C., Integral barrier Lyapunov function based adaptive control for switched nonlinear systems, Science China Information Sciences, 63, 3, 1-14 (2020) · Zbl 1336.93096 · doi:10.1007/s11432-012-4779-0 |
| [14] | Manivannan, A.; Muralisankar, S., Robust stability analysis of Takagi-Sugeno fuzzy nonlinear singular systems with time-varying delays using delay decomposition approach, Circuits, Systems, and Signal Processing, 35, 791-809 (2016) · Zbl 1346.93311 · doi:10.1007/s00034-015-0096-3 |
| [15] | Park, M.; Kwon, O.; Park, J.; Lee, S.; Cha, E., Stability of time-delay systems via Wirtinger-based double integral inequality, Automatica, 55, 204-208 (2015) · Zbl 1377.93123 · doi:10.1016/j.automatica.2015.03.010 |
| [16] | Ren, J.; Tian, Y.; Zhang, Q., Stability analysis and controller synthesis of continuous-time nonhomogeneous Markovian jump systems with state and input delays, Journal of Franklin Institute (2020) · Zbl 1454.93290 · doi:10.1016/j.jfranklin.2020.05.015 |
| [17] | Shen, H.; Li, F.; Cao, J.; Wu, Z.; Lu, G., Fuzzy-model-based output feedback reliable control for network-based semi-Markov jump nonlinear systems subject to redundant channels, IEEE Transactions on Cybernetics (2019) · doi:10.1109/TCYB.2019.2959908 |
| [18] | Shen, H.; Xing, M.; Wu, Z.; Xu, S.; Cao, J., Multi-objective fault-tolerant control for fuzzy switched systems with persistent dwell-time and its application in electric circuits, IEEE Transactions on Fuzzy Systems (2019) · doi:10.1109/TFUZZ.2019.2935685 |
| [19] | Sun, J.; Liu, G.; Chen, J.; Rees, D., Improved delay-range-dependent stability criteria for linear systems with time-varying delays, Automatica, 46, 2, 466-470 (2010) · Zbl 1205.93139 · doi:10.1016/j.automatica.2009.11.002 |
| [20] | Sun, Q.; Han, R.; Zhang, H.; Zhou, J.; Guerrero, J., A multiagent-based consensus algorithm for distributed coordinated control of distributed generators in the energy internet, IEEE Transactions on Smart Grid, 6, 6, 3006-3019 (2015) · doi:10.1109/TSG.2015.2412779 |
| [21] | Sun, Q.; Zhang, N.; You, S.; Wang, J., The dual control with consideration of security operation and economic efficiency for energy hub, IEEE Transactions on Smart Grid, 10, 6, 5930-5941 (2019) · doi:10.1109/TSG.2019.2893285 |
| [22] | Sun, Q.; Zhang, Y.; He, H.; Ma, D.; Zhang, H., A novel energy function-based stability evaluation and nonlinear control approach for energy internet, IEEE Transactions on Smart Grid, 8, 3, 1195-1210 (2017) · doi:10.1109/TSG.2015.2497691 |
| [23] | 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) · doi:10.1016/j.neucom.2017.09.051 |
| [24] | Tang, L.; Li, D. J., Time-varying barrier Lyapunov function based adaptive neural controller design for nonlinear pure-feedback systems with unknown hysteresis, International Journal of Control, Automation and Systems, 17, 7, 1642-1654 (2019) · doi:10.1007/s12555-018-0745-y |
| [25] | Tang, L.; Ma, D.; Zhao, J., Adaptive neural control for switched non-linear systems with multiple tracking error constraints, IET Signal Processing, 13, 3, 330-337 (2019) · doi:10.1049/iet-spr.2018.5077 |
| [26] | Tian, Y.; Wang, Z., A new integral inequality approach for extended dissipative filters design of singular Markovian jump systems with discrete and distributed delay, Circuits, Systems, and Signal Processing, 39, 2900-2921 (2020) · Zbl 1448.93333 · doi:10.1007/s00034-019-01305-9 |
| [27] | Tian, Y.; Wang, Z., A new multiple integral inequality and its application to stability analysis of time-delay systems, Appllied Mathematics Letters (2020) · Zbl 1436.93099 · doi:10.1016/j.aml.2020.106325 |
| [28] | Tian, Y.; Wang, Z., \(####\) performance state estimation for static neural networks with time-varying delays via two improved inequalities, IEEE Transaction on Circuits and Systems II, Express Briefs (2020) · doi:10.1109/TCSII.2020.2995604 |
| [29] | Tian, Y.; Wang, Z., Stability analysis for delayed neural networks based on the augmented Lyapunov-Krasovskii functional with delay-product-type and multiple integral terms, Neurocomputing (2020) · doi:10.1016/j.neucom.2020.05.045 |
| [30] | Tong, S.; Li, Y., Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties, Science China Information Sciences, 53, 307-324 (2010) · Zbl 1497.93134 · doi:10.1007/s11432-010-0031-y |
| [31] | Tong, S.; Li, Y., Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems, Science China Information Sciences, 57, 1-14 (2014) · Zbl 1331.93136 · doi:10.1007/s11432-013-5043-y |
| [32] | Wang, H.; Zhou, B.; Lu, R.; Xue, A., New stability and stabilization criteria for a class of fuzzy singular systems with time-varying delay, Journal of the Franklin Institute, 351, 7, 3766-3781 (2014) · Zbl 1290.93132 · doi:10.1016/j.jfranklin.2013.02.030 |
| [33] | Wang, M.; Wang, C.; Shi, P.; Liu, X., Dynamic learning from neural control for strict-feedback systems with guaranteed predefined performance, IEEE Transactions on Neural Networks and Learning Systems, 27, 12, 2564-2576 (2016) · doi:10.1109/TNNLS.2015.2496622 |
| [34] | Wang, M.; Yang, A., Dynamic learning from adaptive neural control of robot manipulators with prescribed performance, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47, 8, 2244-2255 (2017) · doi:10.1109/TSMC.2016.2645942 |
| [35] | Wang, Y.; Zhang, T.; Ren, J.; Chen, M., Observer-based event triggered sliding mode control for uncertain descriptor systems with a neural-network event-triggering sampling scheme, Neurocomputing, 385, 319-328 (2020) · doi:10.1016/j.neucom.2019.12.066 |
| [36] | Wang, Y.; Zhang, T.; Ren, J.; Li, J., Network-based integral sliding mode control for descriptor systems with event-triggered sampling scheme, International Journal of Robust and Nonlinear Control, 29, 2757-2776 (2019) · Zbl 1418.93053 · doi:10.1002/rnc.4545 |
| [37] | Wu, Z.; Wang, Y., Fuzzy adaptive practical fixed-time consensus for second-order nonlinear multi agent systems under actuator faults, IEEE Transactions on Cybernetics (2020) · doi:10.1109/TCYB.2019.2963681 |
| [38] | Zeng, H.; He, Y.; Wu, M.; She, J., New results on stability analysis for systems with discrete distributed delay, Automatica, 60, 189-192 (2015) · Zbl 1331.93166 · doi:10.1016/j.automatica.2015.07.017 |
| [39] | Zhang, B.; Zheng, W.; Xu, S., Filtering of Markovian jump delay systems based on a new performance index, IEEE Transactions on Circuits and Systems I: Regular Papers, 54, 9, 1250-1263 (2013) · Zbl 1468.94288 · doi:10.1109/TCSI.2013.2246213 |
| [40] | Zhao, C.; Lin, X.; Chen, B.; Wang, Q., A novel Lyapunov-Krasovskii functional approach to stability and stabilization for T-S fuzzy systems with time delay, Neurocomputing, 313, 288-294 (2018) · doi:10.1016/j.neucom.2018.06.024 |
| [41] | Zhi, Y.; He, Y.; Wu, M.; Liu, Q., New results on dissipativity analysis of singular systems with time-varying delay, Information Sciences, 479, 292-300 (2019) · Zbl 1451.93223 · doi:10.1016/j.ins.2018.12.010 |
| [42] | Zhuang, G.; Xu, S.; Zhang, B.; Xia, J.; Chu, Y.; Zou, Y., Unified filters design for singular Markovian jump systems with time-varying delays, Journal of the Franklin Institute, 353, 3739-3768 (2016) · Zbl 1347.93261 · doi:10.1016/j.jfranklin.2016.04.013 |
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.
