Robust local stabilization of discrete time-varying delayed state systems under saturating actuators. (English) Zbl 1451.93286
Summary: This paper deals with discrete time-varying systems with state-delayed and saturating actuators. A robust state feedback control gain is designed through convex methods ensuring the local stability of the time-varying system with interval time-varying state delay. The estimate of the set of admissible initial conditions is characterized by three convex sets allowing less conservative estimates. Through two numerical examples, we compare our approach with others in the literature and illustrate the better behavior of the proposed methods.
MSC:
| 93D09 | Robust stability |
| 93C55 | Discrete-time control/observation systems |
| 93C43 | Delay control/observation systems |
| 93B52 | Feedback control |
Keywords:
time-varying discrete-time systems; time-varying state-delays; saturating input; robust controlReferences:
| [1] | Chen, Y.; Fei, S.; Zhang, K., Stabilisation for switched linear systems with time-varying delay and input saturation, International Journal of Systems Science, 45, 3, 532-546 (2014) · Zbl 1307.93302 |
| [2] | Chen, Y.; Wang, Z.; Fei, S.; Han, Q.-L., Regional stabilization for discrete time-delay systems with actuator saturations via a delay-dependent polytopic approach, IEEE Transactions on Automatic Control, 64, 3, 1257-1264 (2019) · Zbl 1482.93464 |
| [3] | De Souza, C.; Leite, V. J.S.; Silva, L. F.P.; Castelan, E. B., ISS robust stabilization of state-delayed discrete-time systems with bounded delay variation and saturating actuators, IEEE Transactions on Automatic Control, 64, 3913-3919 (2019) · Zbl 1482.93449 |
| [4] | Fridman, E., Introduction to time-delay systems. Systems & control: foundations & applications (2014), Birkhäuser · Zbl 1303.93005 |
| [5] | He, Y.; Wu, M.; Liu, G.-P.; She, J.-H., Output feedback stabilization for a discrete-time system with a time-varying delay, IEEE Transactions on Automatic Control, 53, 10, 2372-2377 (2008) · Zbl 1367.93507 |
| [6] | Hetel, L.; Daafouz, J.; Iung, C., Equivalence between the Lyapunov-Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems, Nonlinear Analysis. Hybrid Systems, 2, 3, 697-705 (2008) · Zbl 1215.93132 |
| [7] | Li, J.; Ma, R.; Dimirovski, G. M.; Fu, J., Dwell-time-based stabilization of switched linear singular systems with all unstable-mode subsystems, Journal of the Franklin Institute, 354, 7, 2712-2724 (2017) · Zbl 1364.93710 |
| [8] | Liu, X.; Wang, F.; Tang, M., Auxiliary function-based summation inequalities and their applications to discrete-time systems, Automatica, 78, 211-215 (2017) · Zbl 1357.93081 |
| [9] | Nam, P.; Pathirana, P.; Trinh, H., Discrete wirtinger-based inequality and its application, International Journal of the Franklin Institute, 352, 1893-1905 (2015) · Zbl 1395.93448 |
| [10] | Pal, V. C.; Negi, R., Delay-dependent stability criterion for uncertain discrete time systems in presence of actuator saturation, Transactions of the Institute of Measurement and Control, 40, 6, 1873-1891 (2018) |
| [11] | Park, P. G.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 235-238 (2011) · Zbl 1209.93076 |
| [12] | Seuret, A., & Gouaisbaut, F. (2014). Integral inequality for time-varying delay systems. In European control conference France. · Zbl 1328.93195 |
| [13] | Seuret, A.; Gouaisbaut, F.; Fridman, E., Stability of discrete-time systems with time-varying delays via a novel summation inequality, IEEE Transactions on Automatic Control, 60, 10, 2740-2745 (2015) · Zbl 1360.93612 |
| [14] | Seuret, A.; Gouaisbaut, F.; Liu, K., Discretized Jensen inequality: an alternative vision of the reciprocally convex combination lemma, IFAC PapersOnLine (2016) |
| [15] | Silva, L. F.P.; Leite, V. J.S.; Castelan, E. B.; Feng, G., Delay dependent local stabilization conditions for time-delay nonlinear discrete-time systems using Takagi-Sugeno models, International Journal of Control, Automation and Systems, 16, 1435-1447 (2018) |
| [16] | Silva, L. F.P.; Leite, V. J.S.; Castelan, E. B.; Klug, M.; Guelton, K., Local stabilization of nonlinear discrete-time systems with time-varying delay in the states and saturating actuators, Information Sciences, 518, 272-285 (2020) · Zbl 1461.93388 |
| [17] | Silva, J. V.V.; Silva, L. F.P.; Rubio Scola, I.; Leite, V. J.S., Robust local stabilization of discrete-time systems with time-varying state delay and saturating actuators, Mathematical Problems in Engineering, 2018, 1-9 (2018), Article ID 5013056 · Zbl 1427.93214 |
| [18] | Sun, Y.; Zhao, J.; Dimirovski, G. M., Adaptive control for a class of state-constrained high-order switched nonlinear systems with unstable subsystems, Nonlinear Analysis. Hybrid Systems, 32, 91-105 (2019) · Zbl 1425.93162 |
| [19] | Tarbouriech, S.; Garcia, G.; Gomes da Silva Jr., J. M.; Queinnec, I., Stability and stabilization of linear systems with saturating actuators (2011), Springer Science & Business Media · Zbl 1279.93004 |
| [20] | Wei, Y.; Zheng, W. X.; Xu, S., Robust output feedback control of uncertain time-delay systems with actuator saturation and disturbances, Journal of the Franklin Institute, 352, 5, 2229-2248 (2015) · Zbl 1395.93184 |
| [21] | Xiao, S.; Xu, L.; Zeng, H.-B.; Teo, K. L., Improved stability criteria for discrete- time delay systems via novel summation inequalities, International Journal of Control, Automation and Systems, 16, 1592-1602 (2018) |
| [22] | Xu, S.; Feng, G.; Zou, Y.; Huang, J., Robust controller design of uncertain discrete time-delay systems with input saturation and disturbances, IEEE Transactions on Automatic Control, 57, 10, 2604-2609 (2012) · Zbl 1369.93208 |
| [23] | Zhang, C.-K.; He, Y.; Jiang, L.; Wu, M.; Zeng, H.-B., Summation inequalities to bounded real lemmas of discrete-time systems with time-varying delay, IEEE Transactions on Automatic Control, 62, 5, 2582-2588 (2017) · Zbl 1366.93169 |
| [24] | Zhang, X.; Zhao, J.; Dimirovski, G. M., \( l_2\)-Gain analysis and control synthesis of uncertain discrete-time switched linear systems with time delay and actuator saturation, International Journal of Control, 84, 10, 1746-1758 (2011) · Zbl 1236.93063 |
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