Finite-time dissipative control of uncertain singular T-S fuzzy time-varying delay systems subject to actuator saturation. (English) Zbl 1448.93288
Summary: This paper investigates the dissipative-based finite-time control for uncertain singular T-S fuzzy time-varying delay system affected by actuator saturation. First, the concept of dissipative stability and finite-time bound is presented. Then an appropriate Lyapunov-Krasovskii functional (LKF) is established and for the sake of reducing the conservatism of the results, some free matrices are introduced. Using the convexity property of the matrix inequality, some conditions are given to ensure the fuzzy system is finite-time bounded and dissipative. Moreover, by solving a series of linear matrix inequalities (LMIs), the controllers with the dissipative disturbance weakened level are derived. Finally, simulation examples are presented to show the feasibility and superiority of this method.
MSC:
| 93D40 | Finite-time stability |
| 93C42 | Fuzzy control/observation systems |
| 93C41 | Control/observation systems with incomplete information |
| 93C43 | Delay control/observation systems |
Keywords:
T-S fuzzy system; dissipative control; optimization problem; actuator saturation; finite timeReferences:
| [1] | Amato, F.; Ariola, M.; Dorato, P., Finite-time control of linear systems subject to parametric uncertainties and disturbances, Automatica, 37, 9, 1459-1463 (2001) · Zbl 0983.93060 · doi:10.1016/S0005-1098(01)00087-5 |
| [2] | Bhat, S.; Bernstein, D., Finite-time stability of continuous autonomous systems, Siam J Control Optim, 38, 751-766 (2006) · Zbl 0945.34039 · doi:10.1137/S0363012997321358 |
| [3] | Cao, Y.; Lin, Z., Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function, Automatica, 39, 1235-1241 (2003) · Zbl 1139.93342 · doi:10.1016/S0005-1098(03)00072-4 |
| [4] | Cheng, J.; Zhu, H., Finite-time filtering for discrete-time markovian jump systems with partly unknown transition probabilities, Can J Phys, 91, 1020-1028 (2013) · doi:10.1139/cjp-2012-0296 |
| [5] | Duan, W.; Cai, C.; Zou, Y.; You, J., Synchronization criteria for singular complex dynamical net works with delayed coupling and non-delayed coupling, Control Theory Appl, 30, 947-955 (2013) · Zbl 1299.93104 |
| [6] | Gassara, H.; Hajjaji, A.; Kchaou, M.; Chaabane, M., Observer \(\left( Q, V, R \right) - \partial \)-dissipative control for T-S fuzzy descriptor systems with time delay, J Franklin Inst, 351, 187-206 (2014) · Zbl 1293.93480 · doi:10.1016/j.jfranklin.2013.07.015 |
| [7] | Gassara, H.; Kchaou, M.; Hajjaji, A., Control of time delay fuzzy descriptor systems with actuator saturation, Circuits Syst Signal Process, 33, 3739-3756 (2014) · Zbl 1342.93074 · doi:10.1007/s00034-014-9836-z |
| [8] | Ge, C.; Shi, Y.; Park, J.; Hua, C., Robust \({H_\infty }\) 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 |
| [9] | Han, C.; Zhang, G.; Wu, L.; Zeng, Q., Sliding mode control of T-S fuzzy descriptor systems with time-delay, J Franklin Inst, 349, 1430-1444 (2012) · Zbl 1254.93042 · doi:10.1016/j.jfranklin.2011.07.001 |
| [10] | Han, C.; Wu, L.; Shi, P.; Zeng, Q., On dissipativity of Takagi-Sugeno fuzzy descriptor systems with time-delay, J Franklin Inst, 349, 3170-3184 (2012) · Zbl 1259.93075 · doi:10.1016/j.jfranklin.2012.10.007 |
| [11] | He, S.; Liu, F., Robust finite-time estimation of Markovian jumping systems with bounded transition probabilities, Appl Math Comput, 222, 297-306 (2013) · Zbl 1329.93142 |
| [12] | Hu, T.; Lin, Z.; Chen, B., Analysis and design for discrete- time linear systems subject to actuator saturation, Syst Control Lett, 45, 97-112 (2002) · Zbl 0987.93027 · doi:10.1016/S0167-6911(01)00168-2 |
| [13] | Ji, X.; Sun, Y.; Su, H., Analysis and design for singular discrete linear systems subject to actuator saturation, Asian J Control, 13, 350-355 (2011) · Zbl 1222.93075 · doi:10.1002/asjc.307 |
| [14] | Kong C, Ma Y, Liu D (2019) Observer-based quantized sliding mode dissipative control for singular semi-Markovian jump systems. Appl Math Comput 362. 10.1016/j.amc.2019.06.053 · Zbl 1433.93126 |
| [15] | Kumar, SV; Raja, R.; Anthoni, SM; Cao, J.; Tu, Z., Robust finite-time non-fragile sampled-data control for T-S fuzzy flexible spacecraft model with stochastic actuator faults, Appl Mat Comput, 321, 483-497 (2018) · Zbl 1426.93164 · doi:10.1016/j.amc.2017.11.001 |
| [16] | Li L Y (1989) Singular control systems, Lecture Notes in Control and Information · Zbl 0669.93034 |
| [17] | Li, L.; Zhang, Q., Finite-time control for singular Markovian jump systems with partly unknown transition rates, Appl Math Model, 254, 106-125 (2015) · Zbl 1335.93075 |
| [18] | Lin, Z.; Lv, L., Set invariance conditions for singular linear systems subject to actuator saturation, IEEE Trans Autom Control, 52, 2351-2355 (2007) · Zbl 1366.93294 · doi:10.1109/TAC.2007.910711 |
| [19] | Ma, Y.; Yan, Y., Observer-based \({H_\infty }\) control for uncertain singular time-delay systems with actuator saturation, Optim Control Appl Methods, 37, 5, 867-884 (2016) · Zbl 1348.93113 · doi:10.1002/oca.2197 |
| [20] | Ma, S.; Zhang, C., \(H_\infty\) control for discrete-time singular Markov jump systems subject to actuator saturation, J Franklin Inst, 349, 1011-1029 (2012) · Zbl 1273.93066 · doi:10.1016/j.jfranklin.2011.12.004 |
| [21] | Ma, Y.; Chen, M.; Zhang, Q., Memory dissipative control for singular T-S fuzzy time- varying delay systems under actuator saturation, J Franklin Inst, 351, 5358-5375 (2015) |
| [22] | Ma, Y.; Fu, L.; Jing, Y., Finite-time \(H_\infty\) control for a class of discrete-time switched singular time-delay systems subject to actuator saturation, Appl Math Comput, 261, 264-283 (2015) · Zbl 1410.93074 |
| [23] | Ma, Y.; Chen, M.; Zhang, Q., Non-fragile static output feedback control for singular T-S fuzzy delay-dependent systems subject to Markovian jump and actuator saturation, J Franklin Inst, 353, 11, 2373-2397 (2016) · Zbl 1347.93164 · doi:10.1016/j.jfranklin.2016.04.006 |
| [24] | Men, Y.; Huang, X.; Wang, Z.; Shen, H.; Chen, B., Quantized asynchronous dissipative state estimation of jumping neural networks subject to occurring randomly sensor saturations, Neurocomputing, 291, 207-214 (2018) · doi:10.1016/j.neucom.2018.02.071 |
| [25] | Su, L.; Ye, D., Mixed \({H_\infty }\) and passive event-triggered reliable control for T-S fuzzy Markov jump systems, Neurocomputing, 281, 96-105 (2013) · doi:10.1016/j.neucom.2017.11.065 |
| [26] | Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE Trans Syst Man Cybern, 15, 116-132 (1985) · Zbl 0576.93021 · doi:10.1109/TSMC.1985.6313399 |
| [27] | Tao, H.; Hu, S., Robust dissipative tolerant-control of Takagi-Sugeno fuzzy systems with actuator saturation, Control Theory Appl, 27, 205-210 (2010) · Zbl 1240.93225 |
| [28] | Tian, G.; Yue, D.; Zhang, G., Delay-dependent robust control for T-S fuzzy system with interval time-varying delay, Fuzzy Sets Syst, 160, 1708-1719 (2009) · Zbl 1175.93134 · doi:10.1016/j.fss.2008.10.014 |
| [29] | Tong Y, Wu B, Huang F (2012) Finite-time boundedness and -gain analysis for linear time-varying singular impulsive systems. In: Chinese Control and Decision Conference, 4031-4035 |
| [30] | Wang, J.; Shen, L.; Xia, J.; Wang, Z.; Chen, X., Asynchronous dissipative filtering for nonlinear jumping systems subject to fading channels, J Franklin Inst, 357, 589-605 (2020) · Zbl 1429.93391 · doi:10.1016/j.jfranklin.2019.09.031 |
| [31] | Weiss, L.; Infante, E., Finite time stability under perturbing forces and on product spaces, IEEE Trans Autom Control, 12, 1, 54-59 (1967) · Zbl 0168.33903 · doi:10.1109/TAC.1967.1098483 |
| [32] | Xing, M.; Xia, J.; Wang, J.; Meng, B.; Shen, H., Asynchronous \({H_\infty }\) filtering for nonlinear persistent dwell-time switched singular systems with measurement quantization, Appl Math Comput, 362, 124578 (2019) · Zbl 1433.93035 |
| [33] | Xing, M.; Xia, J.; Huang, X.; Shen, H., On dissipativity-based filtering for discretetime switched singular systems with sensor failures: a persistent dwell-time scheme, IET Control Theory Appl, 13, 12, 1814-1822 (2019) · Zbl 1432.93219 · doi:10.1049/iet-cta.2018.6376 |
| [34] | Yang, H.; Li, H.; Sun, F.; Yuan, Y., Robust control for Markovian jump delta operator systems with actuator saturation, Eur J Control, 20, 207-215 (2014) · Zbl 1293.93771 · doi:10.1016/j.ejcon.2014.04.004 |
| [35] | Zhang, Y.; Liu, C.; Mu, X., Robust finite-time stabilization of uncertain singular Markovian jump systems, Appl Math Model, 36, 5109-5121 (2012) · Zbl 1252.93130 · doi:10.1016/j.apm.2011.12.052 |
| [36] | Zhang, Y.; Shi, P.; Nguang, SK, Observer-based finite-time \({H_\infty }\) control for discrete singular stochastic systems, Appl Math Lett, 38, 115-121 (2014) · Zbl 1314.93016 · doi:10.1016/j.aml.2014.07.010 |
| [37] | Zhang, Y.; Shi, P.; Nguang, S.; Karimi, H.; Agarwal, R., Robust finite-time fuzzy control for uncertain time-delay systems with stochastic jumps, J Franklin Inst, 351, 4211-4229 (2014) · Zbl 1294.93082 · doi:10.1016/j.jfranklin.2014.04.004 |
| [38] | Zhang, Y.; Shi, Y.; Shi, P., Robust and non-fragile finite-time \({H_\infty }\) control for uncertain Markovian jump nonlinear systems, Appl Math Comput, 279, 125-138 (2016) · Zbl 1410.93142 |
| [39] | Zhang, Y.; Shi, P.; Agarwal, RK; Shi, Y., Event-based mixed \({H_\infty }\) and passive filtering for discrete singular stochastic systems, Intl J Control (2018) · Zbl 1453.93238 · doi:10.1080/00207179.2018.1559360 |
| [40] | Zhang, Y.; Shi, P.; Agarwal, RK; Shi, Y., Event-Based dissipative analysis for discrete time-delay singular jump neural networks, IEEE Trans Neural Netw Learn Syst (2019) · doi:10.1109/TNNLS.2019.2919585 |
| [41] | Zhao, F.; Zhang, Q.; Yan, X.; Cai, M., \({H_\infty }\) filtering for stochastic singular fuzzy systems with time-varying delay, Nonlinear Dyn, 79, 215-228 (2015) · Zbl 1331.93206 · doi:10.1007/s11071-014-1658-9 |
| [42] | Zhu, X.; Xia, Y., Descriptor fault detection filter design for T-S fuzzy discrete-time systems, Journal of the Franklin Institute, 351, 5385-5375 (2014) · Zbl 1393.93076 |
| [43] | Zuo, Z.; Wang, Y.; Yang, W., Gain fault tolerant control of singular Lipschitz systems in the presence of actuator saturation, Int J Robust Nonlinear Control, 25, 1751-1766 (2015) · Zbl 1326.93037 · doi:10.1002/rnc.3165 |
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.
