Abstract
The problem of the decentralized robust control is considered for a class of large-scale time-varying systems withdelayed state perturbations and external disturbances in the interconnections. Here, the upper bounds of the delayed stateperturbations and external disturbances in the interconnections are assumed to be unknown. Adaptation laws areproposed to estimate such unknown bounds; by making use of the updated values of the unknown bounds, decentralized linear and nonlinear memoryless robust state feedback controllers are constructed. Based on Lyapunov stability theoryand Lyapunov–Krasovskii functionals, as well as employing the proposed decentralized nonlinear robust state feedback controllers, it is shown that the solutions of the resulting adaptive closed-loop large-scale time-delay system can be guaranteed to be uniformly bounded and that the states converge uniformly and asymptotically to zero. It is also shown that the proposed decentralized linear robust state feedback controllers can guarantee the uniform ultimate boundedness of the resulting adaptive closed-loop large-scale time-delay system. Finally, a numerical example is given to demonstrate the validity of the results.
Similar content being viewed by others
References
M. S. Mahmoud M. F. Hassan M.G. Darwish (1985) Large-Scale Control Systems: Theories and Techniques Marcel Dekker New York NY
J. Lunze (1992) Feedback Control of Large-Scale Systems Prentice-Hall, Englewood Cliffs New Jersey
D. D. Siljak (1991) Decentralized Control of Complex Systems Academic Press New York, NY
E.J. Davison U. Ozguner (1983) ArticleTitleCharacterizations of Decentralized Fixed Modes for Interconnected Systems Automatica 19 169–182 Occurrence Handle10.1016/0005-1098(83)90089-4
M. Ikeda D. D. Siljak (1980) ArticleTitleDecentralized Stabilization of Linear Time-Varying Systems IEEE Transactions on Automatic Control 25 106–107 Occurrence Handle10.1109/TAC.1980.1102237
W. J. Wang C. F. Cheng T. T. Lee (1989) ArticleTitleStabilization of Large-Scale Systems with Nonlinear Perturbations via Local feedback International Journal of Systems Science 20 1003–1010
Y. H. Chen G. Leitmann X. Z. Kai (1991) ArticleTitleRobust Control Design for Interconnected Systems with Time-Varying Uncertainties International Journal of Control 54 1119–1142
V. B. Kolmanovskii V. R. Nosov (1986) Stability of Functional Differential Equations Academic Press New York, NY
M.Z. Manu J. Mohammad (1987) Time-Delay Systems Analysis, Optimization, and Application AT&T Bell Laboratories New York, NY
A. S. C. Sinha (1990) ArticleTitleStabilization of Large-Scale Nonlinear Infinite-Delay Systems International Journal of Systems Science 21 2679–2684
T. N. Lee U. L. Radovic (1987) ArticleTitleGeneral Decentralized Stabilization of Large-Scale Linear Continuous and Discrete Time-Delay Systems International Journal of Control 46 2127–2140
T. N. Lee U. L. Radovic (1988) ArticleTitleDecentralized Stabilization of Linear Continuous and Discrete-Time Systems with Delays in Interconnections IEEE Transactions on Automatic Control 33 757–761 Occurrence Handle10.1109/9.1293
Wu H.S. Decentralized Output Feedback Control of Large-Scale Interconnected Time-Delay Systems. Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, 2, pp.~1611–1616, 1996.
H. S. Wu (1999) ArticleTitleDecentralized Stabilizing State Feedback Controllers for a Class of Large-Scale Systems Including State Delay in the Interconnections Journal of Optimization Theory and Applications 100 59–87 Occurrence Handle10.1023/A:1021764814535
M. J. Corless G. Leitmann (1983) ArticleTitleAdaptive Control of Systems Containing Uncertain Functions and Unknown Functions with Uncertain Bounds Journal of Optimization Theory and Applications 41 155–168 Occurrence Handle10.1007/BF00934441
C. H. Choi H. S. Kim (1993) ArticleTitleAdaptive Regulations for a Class of Uncertain Systems with Partial Knowledge of Uncertainity Bounds IEEE Transactions on Automatic Control 38 1246–1250 Occurrence Handle10.1109/9.233160
H. S. Wu (1999) ArticleTitleContinous Adaptive Robust Controllers Guaranteeing Uniform Ultimate Boundedness for Uncertain Nonlinear Systems International Journal of Control 72 115–122 Occurrence Handle10.1080/002071799221280
Wu, H. S., Adaptive Robust State FeedbackControllers for a Class of Dynamical Systems with Delayed State Perturbations, Proceedings of the 2000 American Control Conference, Chicago, Illinois: 3661–3665, 2000.
H. S. Wu (2000) ArticleTitleAdaptive Stabilizing State Feedback Controllers of Uncertain Dynamical Systems with Multiple Time Delays IEEE Transactions on Automatic Control 45 1697–1701 Occurrence Handle10.1109/9.880623
H. S. Wu (2002) ArticleTitleDecentralized Adaptive Robust Control for a Class of Large-Scale Systems Including Delayed State Perturbations in the Interconnections IEEE Transactions on Automatic Control 47 1745–1751 Occurrence Handle10.1109/TAC.2002.803551
M. Ikeda H. Maeda S. Kodama (1972) ArticleTitleStabilizations of Linear Systems SIAM Journal on Control and Optimization 10 716–729 Occurrence Handle10.1137/0310052
M. Ikeda T. Ashida (1979) ArticleTitleStabilization of LinearSystems with Time-Varying Delay IEEE Transactions on Automatic Control 24 369–370 Occurrence Handle10.1109/TAC.1979.1102025
J. J. Slotine W. Li (1991) Applied Nonlinear Control Prentice-Hall, Englewood Cliffs New Jersey
J. K. Hale S. M. V. Lunel (1993) Introduction to Funtional Differential Equations Springer Verlag New York, NY
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wu, H.S. Decentralized Adaptive Robust State Feedback for Uncertain Large-Scale Interconnected Systems with Time Delays. J Optim Theory Appl 126, 439–462 (2005). https://doi.org/10.1007/s10957-005-4726-y
Issue Date:
DOI: https://doi.org/10.1007/s10957-005-4726-y