| Title:
|
Decentralized control of interconnected linear systems with delayed states (English) |
| Author:
|
de Souza, Carlos E. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
[309]-323 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper addresses the problems of stability analysis and decentralized control of interconnected linear systems with constant time-delays in the state of each subsystems as well as in the interconnections. We develop delay- dependent methods of stability analysis and decentralized stabilization via linear memoryless state-feedback. The proposed methods are given in terms of linear matrix inequalities. Extensions of the decentralized stabilization result to more complex control problems, such as decentralized static output feedback, decentralized ${\cal H}_{\infty }$ control, decentralized robust stabilization, and decentralized robust ${\cal H}_{\infty }$ control are also discussed. (English) |
| Keyword:
|
time-delay |
| Keyword:
|
stability analysis |
| Keyword:
|
state-feedback |
| Keyword:
|
interconnected linear systems |
| Keyword:
|
robust stabilization |
| Keyword:
|
decentralized control |
| MSC:
|
93A14 |
| MSC:
|
93B36 |
| MSC:
|
93C23 |
| MSC:
|
93D09 |
| idZBL:
|
Zbl 1265.93006 |
| idMR:
|
MR1859088 |
| . |
| Date available:
|
2009-09-24T19:39:47Z |
| Last updated:
|
2015-03-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135411 |
| . |
| Reference:
|
[1] Boyd S., Ghaoui L. El, Feron, E., Balakrishnan V.: Linear Matrix Inequalities in Systems and Control Theory.SIAM, Philadelphia 1994 MR 1284712 |
| Reference:
|
[2] Chen Y. H.: Decentralized robust control for large-scale uncertain systems: A design based on the bound of uncertainty.ASME J. Dynamic Systems Measurement and Control 114 (1992), 1–9 Zbl 0767.93002, 10.1115/1.2896502 |
| Reference:
|
[3] Crusius C. A. R., Trofino A.: Sufficient LMI conditions for output feedback control problems.IEEE Trans. Automat. Control 44 (1999), 1053–1057 Zbl 0956.93028, MR 1690555, 10.1109/9.763227 |
| Reference:
|
[4] Souza C. E. de, Li X.: Delay-dependent robust ${\mathcal H}_{\infty }$ control of uncertain linear state-delayed systems.Automatica 35 (1999), 1313–1321 MR 1829975, 10.1016/S0005-1098(99)00025-4 |
| Reference:
|
[5] Gong Z., Wen, C., Mital D. P.: Decentralized robust controller design for a class of interconnected uncertain systems with unknown bound of uncertainty.IEEE Trans. Automat. Control 41 (1996), 850–854 Zbl 1034.93558, MR 1391781, 10.1109/9.506237 |
| Reference:
|
[6] Hale J., Lunel S. M. V.: Introduction to Functional Differential Equations.Springer–Verlag, New York 1993 Zbl 0787.34002, MR 1243878 |
| Reference:
|
[7] Hmamed A.: Note on the stability of large-scale systems with delays.Internat. J. Systems Sci. 17 (1986), 1083–1087 Zbl 0585.93047, MR 0844944, 10.1080/00207728608926870 |
| Reference:
|
[8] Ho S.-J., Horng I.-R., Chou J.-H.: Decentralized stabilization of large-scale systems with structured uncertainties.Internat. J. Systems Sci. 23 (1992), 425–434 Zbl 0747.93006, MR 1151022, 10.1080/00207729208949218 |
| Reference:
|
[9] Ikeda M., Siljak D. D.: Decentralized stabilization of linear time-varying systems.IEEE Trans. Automat. Control 25 (1980), 106–107 Zbl 0446.93039, MR 0561351, 10.1109/TAC.1980.1102237 |
| Reference:
|
[10] Lee T. N., Radovic U. L.: Decentralized stabilization of linear continuous and discrete-time systems with delays in interconnections.IEEE Trans. Automat. Control 33 (1988), 757–761 Zbl 0649.93055, MR 0950798, 10.1109/9.1293 |
| Reference:
|
[11] Li X., Souza C. E. de: Robust stabilization and ${\mathcal H}_{\infty }$ control for uncertain linear time-delay systems.In: Proc. 13th IFAC World Congress, San Francisco 1996, pp. 113–118 |
| Reference:
|
[12] Li X., Souza C. E. de: Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach.IEEE Trans. Automat. Control 42 (1997), 144–1148 Zbl 0889.93050, MR 1469075 |
| Reference:
|
[13] Li X., Souza C. E. de: Criteria for robust stability and stabilization of uncertain linear systems with state delay.Automatica 33 (1997), 1657–1662 MR 1481824, 10.1016/S0005-1098(97)00082-4 |
| Reference:
|
[14] Sandell N. R., Varaiya P., Athans, M., Safonov M. G.: Survey of decentralized control methods for large scale systems.IEEE Trans. Automat. Control 23 (1978), 108–128 Zbl 0385.93001, MR 0490108, 10.1109/TAC.1978.1101704 |
| Reference:
|
[15] Schoen G. M., Geering H. P.: A note on robustness bounds for large-scale time-delay systems.Internat. J. Systems Sci. 26 (1995), 2441–2444 Zbl 0850.93691, 10.1080/00207729508929181 |
| Reference:
|
[16] Siljak D. D.: Large–Scale Dynamic Systems: Stability and Structure.North–Holland, New York 1978 Zbl 0384.93002, MR 0595867 |
| Reference:
|
[17] Su J. H.: Further results on the robust stability of linear systems with a single time delay.Systems Control Lett. 23 (1994), 375–379 Zbl 0805.93045, MR 1303587, 10.1016/0167-6911(94)90071-X |
| Reference:
|
[18] Su T. J., Huang C. G.: Robust stability of delay dependence for linear uncertain systems.IEEE Trans. Automat. Control 37 (1992), 1656–1659 Zbl 0770.93077, MR 1188782, 10.1109/9.256406 |
| Reference:
|
[19] Suh I. H., Bien Z.: A note on the stability of large scale systems with delays.IEEE Trans. Automat. Control 27 (1982), 256–258 Zbl 0469.93008, MR 0680343, 10.1109/TAC.1982.1102817 |
| Reference:
|
[20] Wang S. H., Davison E. J.: On the stabilization of decentralized control systems.IEEE Trans. Automat. Control AC-18 (1973), 473–478 Zbl 0347.93030, MR 0441480, 10.1109/TAC.1973.1100362 |
| Reference:
|
[21] Wang W.-J., Cheng C.-F.: Robustness of perturbed large-scale systems with local constant state feedback.Internat. J. Control 50 (1989), 373–384 Zbl 0683.93026, MR 1014791, 10.1080/00207178908953367 |
| Reference:
|
[22] Xu B., Fu, Y., Bai L.: Further results on robust bounds for large-scale time-delay systems with structured and unstructured uncertainties.Internat. J. Systems Sci. 27 (1996), 1491–1495 Zbl 0874.93079, 10.1080/00207729608929356 |
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