Abstract
For a class of interconnected time-delay uncertain systems satisfing the matching conditions, the sufficient condition for decentralized stabilization feedback control laws is derived based on Lyapunov stability theorem. This condition is expressed as the solvability problem of linear matrix inequalities(LMI). It can be easily determined whether or not, it is feasible and one can easily obtain the decentralized stabilizing state feedback matrices via LMI techniques. The method overcomes the limitations of the existing algebraic Riccati equation method. The given example shows the application of the method.
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References
Jamshidi M. Large-scale systems, modeling and control[M]. Elsevier Science Publishing Co Inc, 1983
Lee T N, Radovic U L. General decentralized stabilization of large-scale linear continuous and discrete time-delay systems[J]. Int J Control, 1987, 46(6): 2127–2140
Lee T N, Radovic U L. Decentralized stabilization of linear continuous and discrete-time systems with delay in interconnections[J]. IEEE Trans Automat Contr, 1988, AC-33(8): 757–761
Trinh H, Aldeen M A. A comment on “Decentralized stabilization of large scale interconnected systems with delays”[J]. IEEE Trans Automat Contr, 1995, AC-40(5): 914–916
Yu L, Chen G D. Decentralized stabilizable controller design for a class of interconnected time-delay[J]. Control and Decision (in Chinese), 1997, 12(5): 559–564
Chen Y H, Leitmann G, Kai X Z. Robust control design for interconnected system with time-varying uncertainties[J]. Int J Contr, 1991, 54(5): 1119–1142
Lin S, Sunil K S. Decentralized control for interconnected uncertain systems: extensions to higher-order uncertainties[J]. Int J Contr, 1993, 57(6): 1453–1468
Wu H S. Decentralized robust control for a class of large-scale interconnected systems with uncertainties[J]. Int J Syst Sci, 1989, 20(12): 2597–2603
Hu S SH, Tang J Q. Decentralized robust suboptional control for a class of interconnected perturbed large-scale systems. Control and Design (in Chinese), 1992, 7(5): 336–347
Boyd Stephen. Linear matrix inequalities in system and control theory[M]. Philadelphia: SIAM, 1994
Iwasaki T, Skelton R E. All controllers for the general Hτ control problem: LMI existence conditions and state space formulas[J]. Automatica, 1994, 30(8): 1307–1317
Wang Y Y, Xie L H, E de Souza. Robust control of uncertain nonlinear systems[J]. Systems and Control Letters, 1992, 19: 139–149
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Foundation item: The National Science Foundation of China(No. 69274005)
Biography of the first author: TANG Zhao-hui, born in Oct. 1965, majoring in linear matrix inequality theory and application, decentralized control and modern robust control, computer control system.
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Tang, Zh., Wu, M., Gui, Wh. et al. Decentralized robust control for large scale interconnected uncertain systems with time-delay. J Cent. South Univ. Technol. 7, 49–52 (2000). https://doi.org/10.1007/s11771-000-0014-z
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DOI: https://doi.org/10.1007/s11771-000-0014-z