Previous |  Up |  Next


decentralized variable structure control; uncertain large-scale systems; time-delayed systems; unmatched uncertainty
Many real-world systems contain uncertainties and with time-varying delays, also, they have become larger and more complicated. Hence, a new decentralized variable structure control law is proposed for a class of uncertain large-scale system with time varying delay in the interconnection and time varying unmatched uncertainties in the state matrix. The proposed decentralized control law for the large-scale time-varying delay system is realized independently through the delayed terms and it can drive the trajectories of the investigated systems onto the sliding mode. Further, the proposed control law can be successfully applied to stabilize a class of uncertain large-scale time-varying delay system with matched and unmatched uncertainties. The so-called sliding coefficient matching condition can be extended for the decentralized variable structure control of the uncertain large-scale time-varying delay systems. Furthermore, in the sliding mode, the investigated system with matched and unmatched uncertainties still bears the insensitivity to the uncertainties and disturbances, which is the same as the systems with just matched uncertainties do. Finally, an illustrative example is given to verify the validity of the proposed decentralized variable structure control law. It has been shown that the proposed decentralized control law is effective for all subsystems of the investigated system. However, the traditional decentralized variable structure control law is not applicable to the investigated system with unmatched uncertainties. It is worth noting that the traditional large-scale system is only a special case in this work.
[1] Chou, C. H., Cheng, C. C.: Design of adaptive variable structure controllers for perturbed time-varying state delay systems. J. Franklin Inst. 338 (2001), 35–46. DOI 10.1016/S0016-0032(00)00070-3 | MR 1815709 | Zbl 0966.93101
[2] Chou, C. H., Cheng, C. C.: A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems. IEEE Trans. Automat. Control 48 (2003), 1213–1217. DOI 10.1109/TAC.2003.814263 | MR 1988091
[3] Chen, W., Li, J.: Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans. Systems Man Cybernet. 38 (2008), 258–266. DOI 10.1109/TSMCB.2007.904544
[4] Ding, Z.: Decentralized output regulation of large scale nonlinear systems with delay. Kybernetika 45 (2009), 33–48. MR 2489579 | Zbl 1158.93303
[5] Fridman, E., Shaked, U.: An improved stabilization method for linear time-delay systems. IEEE Trans. Automat. Control 47 (2002), 1931–1937. DOI 10.1109/TAC.2002.804462 | MR 1937712
[6] Hsu, K. C.: Decentralized variable structure model-following adaptive control for interconnected systems with series nonlinearities. Internat. J. Systems Sci. 29 (1998), 365–372. DOI 10.1080/00207729808929529
[7] Hsu, K. C.: Adaptive variable structure control design for uncertain time-delay systems with nonlinear input. Dynamics and Control 8 (1998), 341–354. DOI 10.1023/A:1008256611126 | MR 1644236
[8] Hsu, K. C.: Decentralized sliding mode control for large-scale time-delayed systems with series nonlinearities. ASME J. Dynamic Systems, Measurement, and Control 121 (1999), 708–713. DOI 10.1115/1.2802539
[9] Hua, C., Wang, Q., Guan, X.: Memoryless state feedback controller design for time delay systems with matched uncertain nonlinearities. IEEE Trans. Automat. Control 53 (2008), 801–807. DOI 10.1109/TAC.2008.917658 | MR 2401033
[10] Hung, J. Y., Gao, W. B., Hung, J. C.: Variable structure control: A survey. IEEE Trans. Ind. Electronics 40 (1993), 2–22. DOI 10.1109/41.184817
[11] Luo, N., Sen, M. Dela: State feedback sliding mode control of a class of uncertain time delay systems. IEE Proc. Part D – Control Theory Appl. 140 (1993), 261–274. DOI 10.1049/ip-d.1993.0035
[12] Mahmoud, M. S.: Stabilizing control for a class of uncertain interconnected systems. IEEE Trans. Automat. Control 39 (1994), 2484–2488. DOI 10.1109/9.362842 | MR 1337577 | Zbl 0825.93628
[13] Petersen, I. R.: Robust $H_\infty $ control of an uncertain system via a stable decentralized output feedback controller. Kybernetika 45 (2009), 101–120. MR 2489583 | Zbl 1158.93328
[14] Petersen, I. R.: A stabilization algorithm for a class of uncertain linear systems. Systems Control Lett. 8 (1987), 351–357. DOI 10.1016/0167-6911(87)90102-2 | MR 0884885 | Zbl 0618.93056
[15] Shyu, K. K., Chen, Y. C.: Robust tracking and model following for uncertain time-delay systems. Internat. J. Control 62 (1995), 589–600. DOI 10.1080/00207179508921558 | MR 1619686 | Zbl 0830.93026
[16] Shyu, K. K., Liu, W. J., Hsu, K. C.: Decentralized variable structure control of zncertain large-scale systems containing a dead-zone. IEE Proc. Part D – Control Theory Appl. 150 (2003), 467–475. DOI 10.1049/ip-cta:20030758
[17] Shyu, K. K., Liu, W. J., Hsu, K. C.: Design of large-scale time-delayed systems with dead-zone input via variable structure control. Automatica 41 (2005), 1239–1246. DOI 10.1016/j.automatica.2005.03.004 | MR 2160123 | Zbl 1080.93003
[18] Siljak, D. D.: Decentralized Control of Complex Systems. Academic, San Diego 1991. MR 1086632
[19] Sun, X. M., Wang, W., Liu, G. P., Zhao, J.: Stability analysis for linear switched systems with time-varying delay. IEEE Trans. Systems Man Cybernet. 38 (2008), 528–533. DOI 10.1109/TSMCB.2007.912078
[20] Tao, C. W., Wang, W. Y., Chan, M. L.: Design of sliding mode controllers for bilinear systems with time varying uncertainties. IEEE Trans. Systems Man Cybernet. 34 (2004), 639–645. DOI 10.1109/TSMCB.2002.805805
[21] Wu, J., Weng, Z., Tian, Z., Shi, S.: Fault tolerant control for uncertain time-delay systems based on sliding mode control. Kybernetika 44 (2008), 617–632. MR 2479308 | Zbl 1180.93087
[22] Xu, S., Lam, J.: On equivalence and efficiency of certain stability criteria for time-delay systems. IEEE Trans. Automat. Control 52 (2007), 95–101. DOI 10.1109/TAC.2006.886495 | MR 2286766
[23] Yan, J., Tsai, J. S., Kung, F.: Robust decentralized stabilization of large-scale delay systems via sliding mode control. ASME J. Dynamic Systems, Measurement, and Control 119 (1997), 307–312. DOI 10.1115/1.2801253 | Zbl 0882.93002
[24] Young, K. D., Utkin, V. I., Özgüner, Ü.: A control engineer’s guide to sliding mode control. IEEE Trans. Control Systems Technology 7 (1999), 328–342. DOI 10.1109/87.761053
[25] Zheng, F., Wang, Q.-G., Lee, T. H.: Adaptive robust control of uncertain time delay systems. Automatica 41 (2005), 1375–1383. DOI 10.1016/j.automatica.2005.03.014 | MR 2160482 | Zbl 1086.93029
Partner of
EuDML logo