Abstract
The problem of the decentralized stabilization of a class of large-scale nonlinear and linear systems including time-varying delays in the interconnections is considered. By combining the Razumikhin-type theorem with the Lyapunov stability theory, we propose a class of decentralized state feedback controllers which can guarantee always some type of stability of large-scale time-delay systems. In this paper, we assume that the time-varying delays are continuous and bounded nonnegative functions. Furthermore, since the proposed decentralized state feedback controllers are independent of the delays, the results obtained in this paper are applicable to systems without exact knowledge of the delays, i.e., systems with perturbed delays. Finally, a numerical example is given to demonstrate the validity of the results.
Similar content being viewed by others
References
Siljak, D. D., Large-Scale Dynamic Systems: Stability and Structure, North-Holland, Amsterdam, Holland, 1978.
Mahmoud, M. S., Hassan, M. F., and Darwish, M. G., Large-Scale Control Systems: Theories and Techniques, Marcel Dekker, New York, New York, 1985.
Davison, E. J., The Decentralized Stabilization and Control of a Class of Unknown Nonlinear Time-Varying Systems, Automatica, Vol. 10, pp. 309–316, 1974.
Siljak, D. D., and Vukcevic, M. B., Decentrally Stabilizable Linear and Bilinear Large-Scale Systems, International Journal of Control, Vol. 26, pp. 289–305, 1977.
Ikeda, M., and Siljak, D. D., Decentralized Stabilization of Linear Time-Varying Systems, IEEE Transactions on Automatic Control, Vol. 25, pp. 106–107, 1980.
Shi, Z. C., and Gao, W. B., Decentralized Stabilization of Time-Varying Large-Scale Interconnected Systems, International Journal of Systems Science, Vol. 18, pp. 1523–1535, 1987.
Feliachi, A., and Thowsen, A., Memoryless Stabilization of Linear Delay Differential Systems, IEEE Transactions on Automatic Control, Vol. 26, pp. 586–587, 1981.
Mori, T., Noldus, E., and Kuwahara, M., A Way to Stabilize Linear Systems with Delayed State, Automatica, Vol. 19, pp. 571–573, 1983.
Ikeda, I., and Ashida, T., Stabilization of Linear Systems with Time-Varying Delay, IEEE Transactions on Automatic Control, Vol. 24, pp. 369–370, 1979.
Watanabe, K., Ito, M., Kaneko, M., and Ouchi, T., Finite Spectrum Assignment Problem for Systems with Delay in State Variable, IEEE Transactions on Automatic Control, Vol. 28, pp. 506–508, 1983.
Kwon, W. H., and Pearson, A. E., Feedback Stabilization of Linear Systems with Delay Control, IEEE Transactions on Automatic Control, Vol. 25, pp. 266–269, 1980.
Sinha, A. S. C., Stabilization of Large-Scale Nonlinear Infinite-Delay Systems, International Journal of Systems Science, Vol. 21, pp. 2679–2684, 1990.
Lee, T. N., and Radovic, U. L., General Decentralized Stabilization of Large-Scale Linear Continuous and Discrete Time-Delay Systems, International Journal of Control, Vol. 46, pp. 2127–2140, 1987.
Lee, T. N., and Radovic, U. L., Decentralized Stabilization of Linear Continuous and Discrete-Time Systems with Delays in Interconnections, IEEE Transactions on Automatic Control, Vol. 33, pp. 757–761, 1988.
Hale, J. K., and Lunel, S. M. V., Introduction to Functional Differential Equations, Springer Verlag, New York, New York, 1993.
Xu, B., and Liu, Y., An Improved Razumikhin-Type Theorem and Its Applications, IEEE Transactions on Automatic Control, Vol. 39, pp. 839–841, 1994.
Gutman, S., Uncertain Dynamical Systems: A Lyapunov Min-Max Approach, IEEE Transactions on Automatic Control, Vol. 24, pp. 437–443, 1979.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wu, H.S. Decentralized Stabilizing State Feedback Controllers for a Class of Large-Scale Systems Including State Delays in the Interconnections. Journal of Optimization Theory and Applications 100, 59–87 (1999). https://doi.org/10.1023/A:1021764814535
Issue Date:
DOI: https://doi.org/10.1023/A:1021764814535