# Article

 Title: Decentralized control for large-scale systems with time-varying delay and unmatched uncertainties (English) Author: Liu, Wen-Jeng Language: English Journal: Kybernetika ISSN: 0023-5954 Volume: 47 Issue: 2 Year: 2011 Pages: 285-299 Summary lang: English . Category: math . Summary: 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. (English) Keyword: decentralized variable structure control Keyword: uncertain large-scale systems Keyword: time-delayed systems Keyword: unmatched uncertainty MSC: 93A15 MSC: 93B12 MSC: 93C10 MSC: 93D05 idZBL: Zbl 1242.93007 idMR: MR2828578 . Date available: 2011-06-06T15:00:47Z Last updated: 2013-09-22 Stable URL: http://hdl.handle.net/10338.dmlcz/141573 . Reference: [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. Zbl 0966.93101, MR 1815709, 10.1016/S0016-0032(00)00070-3 Reference: [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. 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