Abstract
In this paper, we propose a design method of guaranteed cost controllers for uncertain large-scale systems with time delays in subsystem interconnections using delayed feedback. Using the Lyapunov method, a linear matrix inequality (LMI) optimization problem is formulated to design a delayed feedback controller which minimizes the upper bound of a given quadratic cost function. A numerical example is included to illustrate the design procedures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
IKEDA, M., and SILJAK, D. D., Decentralized Stabilization of Large-Scale Systems with Time Delay, Large Scale Systems, Vol. 1, pp. 273–279, 1980.
BAKULE, L., Decentralized Stabilization of Uncertain Delayed Interconnected Systems, Proceeding of the 7th IFAC/IFORMS/IMACS Symposium on Large-Scale Systems: Theory and Applications, London, UK, pp. 575–580, 1980.
DE SOUZA, C. E., and LI, X., An LMI Approach to Decentralized Stabilization of Interconnected Time-Delay Systems, Proceedings of the 38th Conference on Decision and Control, Phoenix, Arizona, pp. 4700–4705, 1999.
TASY, J. T., LIU, P. L., and SU, T. J., Robust Stability for Perturbed Large-Scale Time-Delay Systems, IEE Proceedings-Control Theory and Applications, Vol. 143, pp. 233–236, 1996.
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, Vol. 100, pp. 59–87, 1999.
WON, S., and PARK, J. H., Observer-Based Controller Design for Uncertain Large-Scale Systems with Time Delays in Subsystems Interconnections, JSME International Journal, Vol. 42C, pp. 123–128, 1999.
PARK, J. H., Robust Nonfragile Decentralized Controller Design for Uncertain Large-Scale Interconnected Systems with Time Delays, Journal of Dynamic Systems, Measurements, and Control, Vol. 123, pp. 332–336, 2002.
PARK, J. H., Robust Decentralized Stabilization of Uncertain Large-Scale Discrete-Time Systems with Delays, Journal of Optimization Theory and Applications, Vol. 113, pp. 105–119, 2002.
MORI, T., Criteria for Asymptotic Stability of Linear Time-Delay Systems, IEEE Transactions on Automatic Control, Vol. 30, pp. 158–161, 1985.
CHANG, S. S. L., and PENG, T. K. C., Adaptive Guaranteed Cost Control of Systems with Uncertain Parameters, IEEE Transactions on Automatic Control, Vol. 17, pp. 474–483, 1972.
YU, L., and CHU, J., An LMI Approach to Guaranteed Cost Control of Linear Uncertain Time-Delay Systems, Automatica, Vol. 35, pp. 1155–1159, 1999.
PARK, J. H., Robust Guaranteed Cost Control for Uncertain Linear Differential Systems of Neutral Type, Applied Mathematics and Computation, Vol. 140, pp. 523–535, 2003.
MOHEIMANI, S. O. R., and PETERSEN, I. R., Optimal Quadratic Guaranteed Cost Control of a Class of Uncertain Time-Delay Systems, IEE Proceedings-Control Theory and Applications, Vol.144, pp. 183–188, 1997.
LEE, Y. S., MOON, Y. S., and KWON, W. H., Delay-Dependent Guaranteed Cost Control for Uncertain State-Delayed Systems, Proceedings of the American Control Conference, pp. 3376–3381, 2001.
MOON, Y. S., PARK, P., and KWON, W. H., Robust Stabilization of Uncertain Input-Delayed Systems Using the Reduction Method, Automatica, Vol. 37, pp. 307–312, 2001.
AZUMA, T., IKEDA, K., KONDO, T., and UCHIDA, K., Memory State Feedback Control Synthesis for Linear Systems with Time Delay via a Finite Number of Linear Matrix Inequalitites, Computers and Electrical Engineering, Vol. 28, pp. 217–228, 2002.
BOYD, S., EL GHAOUI, L., FERON, E., and BALAKRISHNAN, V., Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pennsylvania, 1994.
HALE, J., and VERDUYN-LUNEL, S. M., Introduction to Functional Differential Equations, Springer Verlag, New York, NY, 1993.
GU, K., An Integral Inequality in the Stability Problem of Time-Delay Systems, Proceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia, pp. 2805–2810, 2000.
YUE, D., and WON, S., Delay-Dependent Robust Stability of Stochastic Systems with Time Delay and Nonlinear Uncertainties, Electronics Letters, Vol. 37, pp. 992–993, 2001.
GAHINET, P., NEMIROVSKII, A., LAUB, A., and CHILALI, M., LMI Control Toolbox, The Mathworks, Natick, Massachusetts, 1995.
XIE, S., XIE, L. WANG, Y., and ZHANG, H., Decentralized Guaranteed Cost Control of a Class of Large-Scale Interconnected Systems, Proceedings of the 38th Conference on Decision and Control, Phoenix, Arizona, pp. 3297–3302, 1999.
MUKAIDANI, H., TAKATO, Y., TANAKA, Y., and MIZUKAMI, K., An LMI Approach to Guranteed Cost Control of Nonlinear Large-Scale Uncertain Delay Systems under Controller Gain Perturbations, Proceedings of 3rd International DCDIS Conference, Ontario, Canada, pp. 40–45, 2003.
MUKAIDANI, H., An LMI Approach to Decentralized Guaranteed Cost Control for a Class of Uncertain Nonlinear Large-Scale Delay Systems, Journal of Mathematical Analysis and Applications, Vol. 300, pp. 17–29, 2004.
CAO, Y. Y., SUN, Y. X., and LAM, J., Delay-Dependent Robust H ∞ Control for Uncertain Systems with Time-Varying Delays, IEEE Proceedings-Control Theory and Applications, Vol. 145, pp. 338–343, 1998.
Author information
Authors and Affiliations
Additional information
Communicated by Q. C. Zhao
The authors thank the Associate Editor and three anonymous referees for careful reading and useful suggestions.
Rights and permissions
About this article
Cite this article
Kown, O.M., Park, J.H. Decentralized Guaranteed Cost Control for Uncertain Large-Scale Systems Using Delayed Feedback: LMI Optimization Approach. J Optim Theory Appl 129, 391–414 (2006). https://doi.org/10.1007/s10957-006-9075-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10957-006-9075-y